@@AlexPies1 I wrote my answer 3 minutes after his post long before he gave his demo! Display videos by most recent first you will see that I was th first who answered
that's what i did, and i have no idea why he didn't do that. it makes it so much easier to see that things cancel out nicely, leaving you with 16/2 = 8
Yes, not sure how he missed that. But even missing that then distributing the 14 to get 210 was also more complicated because at that point it should be obvious now you have a numerator of "14(15 + sqrt(29) + 1 - sqrt(29))" and this just cancels to 14(16). He completely missed the opportunities for cancelling for a few steps.
8 We can get the value of root x by using quadratic equation formula but notice root x is always bigger than or equal to zero then we can make direct substitution.
If you replace the "7" with a parameter, "k", the answer will be k+1, which I suspected might be the case when I did a "guess and check" on a modified version of the problem where I first replaced the 7's with 6's: 9-3=6 and 9-2=7. So first I did guess and check with 6's in place of the 7's; then I used method 2 on the actual problem, considering the 7's as a parameter.
Slightly quicker than the 2nd method but equivalent: The awkward part of x - 7/√x is the 7/√x, but we can derive that from the first equation by dividing both sides by √x (since √x ≠ 0). x - √x = 7 so dividing by √x, we get √x - 1 = 7/√x. Immediately we now know that x - 7/√x = x - (√x - 1) = x - √x + 1. But x - √x = 7, so the value of x - 7/√x = 7 + 1 = 8.
Steve Prowse'method: 1º) Divide both sides of the first equation by √x: x - √x = 7 ⇒ x/√x - √x/√x = 7/√x ⇒ x/√x - 1 = 7/√x ⇒ 2º) Add (x -7/√x ) to both sides: ⇒ x - 7/√x + x/√x - 1 = 7/√x - 7/√x + x ⇒ x - 7/√x = x - x/√x + 1 ⇒ Rationalizing the denominator of the fraction x/√x: x - 7/√x = (x - √x) + 1 ⇒ 7 + 1 = 8.
Given: x - √x = 7 To find: x - 7/√x Substituting for 7: x - (x - √x)/√x Dividing by √x as √x ≠ 0 by definition: = x - √x + 1 Back-substituting for 7: = 7 + 1 = 8 x - 7/√x = 8. EDIT how did I mess up dividing
Continuing: x - √x = 7 Substituting √x = t t² - t = 7 t² - t - 7 = 0 Using quadratic formula: t = ½ ± √(¼ + 7) t = (½ ± ½√29) As √x = t, x = t² = ½·(15 ± √29).
Complicated solution! No wander people don't like math! From the given equation x - 7 = root (x). Then in root (x) + 7 - 7/root(x) just write common denominator to get x = 8.
I rewrote the first equation to x - 7 = sqrt(x). Then I divided both sides by sqrt(x) giving me sqrt(x) - 7/sqrt(x) = 1. Now you can add the original equation to this to get x - sqrt(x) + sqrt(x) - 7/sqrt(x) = 7 + 1 = 8. The LHS reduces to x - 7/sqrt(x), so x - 7/sqrt(x) = 8.
Let y = sqrt(x), then y^2 - y = 7. x - 7/sqrt(x) = y^2 - 7/y = y^2 - (y^2 - y)/y = y^2 - y + 1 = 7 + 1 = 8. Why do we need other methods? The objective is NOT finding the value of y. ...
Why make it complicated when you can make it simple ? x=7+square(x) , 7/square(x)=square(x)-1 , therefore 7+square(x)-[square(x)-1]= 7+1 . Am I not right ?
In general, if we have x - sqrt x = a and we want to find x - a/sqrtx, this is a + 1. I think that you already have been a video where x = 5. You should remember that ☺️
Sorry, pointless video. Your second solution just begs to be applied from the very beginning and it looks like I'm not the only one who did it. I liked your many other videos but this was just waste.
Third method. Divide the first equation by root x and then take both sides away from x. 8 drops out.
Replace 7 by x- √x in the expression and simplify ---> x - (x-√x)/√x = x -(√x -1) = x - √x +1 = 8
that's... that's what he did
@@AlexPies1 I wrote my answer 3 minutes after his post long before he gave his demo!
Display videos by most recent first you will see that I was th first who answered
I solved this problem in undergrad almost 25 years ago. So nana nana boo boo.
I managed to solve this question in the hospital room minutes after my own birth
At 5:00 you can simplify the second fraction immediately, which automatically will create a common denominator of 2.
that's what i did, and i have no idea why he didn't do that. it makes it so much easier to see that things cancel out nicely, leaving you with 16/2 = 8
Was thinking the same and was really confused on why he didn't do this.
Yes, not sure how he missed that. But even missing that then distributing the 14 to get 210 was also more complicated because at that point it should be obvious now you have a numerator of "14(15 + sqrt(29) + 1 - sqrt(29))" and this just cancels to 14(16). He completely missed the opportunities for cancelling for a few steps.
Shortest method: divide both sides of
x −√x = 7
by √x to get
√x − 1 = 7/√x
Hence
x − 7/√x = x − (√x − 1) = x − √x + 1 = 7 + 1 = 8
The answer must be 8 .
X-sqrt(X) + 1 = 7+1 = 8
It was fun to see a nice number fall out from method 1, then the elegant substitution in method 2. Double fun!
Whenever method one seems overly complicated, I know method two is going to be slick.
8
We can get the value of root x by using quadratic equation formula but notice root x is always bigger than or equal to zero then we can make direct substitution.
If you replace the "7" with a parameter, "k", the answer will be k+1, which I suspected might be the case when I did a "guess and check" on a modified version of the problem where I first replaced the 7's with 6's: 9-3=6 and 9-2=7. So first I did guess and check with 6's in place of the 7's; then I used method 2 on the actual problem, considering the 7's as a parameter.
Slightly quicker than the 2nd method but equivalent: The awkward part of x - 7/√x is the 7/√x, but we can derive that from the first equation by dividing both sides by √x (since √x ≠ 0).
x - √x = 7 so dividing by √x, we get √x - 1 = 7/√x.
Immediately we now know that x - 7/√x = x - (√x - 1) = x - √x + 1.
But x - √x = 7, so the value of x - 7/√x = 7 + 1 = 8.
It's 8. How? Look at the second formula. We substitute 7 with x-√x from the first formula. Then we have x-7/√x＝x-(x-√x)/√x＝x-√x+1＝7+1＝8.
At 5:00 instead of making a common denominator, just do the division (14 / 28) of the second term and you end up with (15 + 1) / 2...
Third method: We have x-√x=7 (Eq 1) Divide on both sides by √x then √x-7/√x= 1 (Eq 2). I add Eq 1 + Eq 2 and I have x-7/√x=8
I did the same
Steve Prowse'method: 1º) Divide both sides of the first equation by √x: x - √x = 7 ⇒ x/√x - √x/√x = 7/√x ⇒ x/√x - 1 = 7/√x ⇒ 2º) Add (x -7/√x ) to both sides: ⇒ x - 7/√x + x/√x - 1 = 7/√x - 7/√x + x ⇒ x - 7/√x = x - x/√x + 1 ⇒ Rationalizing the denominator of the fraction x/√x: x - 7/√x = (x - √x) + 1 ⇒ 7 + 1 = 8.
We can also rearrange and solve x -√x =7 >>>>> x-7 =√x and square both sides
Using the Lambert-Tsallis Wq function: x = Wq(7)^2 = (15+sqrt(29))/2 with q = 0.
Elinize dilinize sağlık hocam
Saolasın ☺️
Given:
x - √x = 7
To find:
x - 7/√x
Substituting for 7:
x - (x - √x)/√x
Dividing by √x as √x ≠ 0 by definition:
= x - √x + 1
Back-substituting for 7:
= 7 + 1
= 8
x - 7/√x = 8.
EDIT how did I mess up dividing
Continuing:
x - √x = 7
Substituting √x = t
t² - t = 7
t² - t - 7 = 0
Using quadratic formula:
t = ½ ± √(¼ + 7)
t = (½ ± ½√29)
As √x = t,
x = t² = ½·(15 ± √29).
Ah wait t can't be negative, so the negative branch is wrong in both t and x.
Complicated solution! No wander people don't like math! From the given equation x - 7 = root (x). Then in root (x) + 7 - 7/root(x) just write common denominator to get x = 8.
I rewrote the first equation to x - 7 = sqrt(x). Then I divided both sides by sqrt(x) giving me sqrt(x) - 7/sqrt(x) = 1. Now you can add the original equation to this to get x - sqrt(x) + sqrt(x) - 7/sqrt(x) = 7 + 1 = 8. The LHS reduces to x - 7/sqrt(x), so x - 7/sqrt(x) = 8.
Instead of doing many pages of work, just graph it for values of X from 0 to 12
X approximately equal 10.2
It would have been much easier to divide by 14 in both the numerator and denominator of the right fraction in the last expression in method 1 😊
nice first time I actually saw the 2nd method first
The second method is scary
Gde je znak jednako?
Too easy Syber it’s 8 all day.
Very poor fraction algebra at the end of 1st method: 14/28=1/2.
Let y = sqrt(x), then y^2 - y = 7.
x - 7/sqrt(x) = y^2 - 7/y = y^2 - (y^2 - y)/y = y^2 - y + 1 = 7 + 1 = 8.
Why do we need other methods? The objective is NOT finding the value of y.
...
Dai dati ho (dividendo per sqrtx)sqrtx-1=7/sqrtx perciò risulta x-(sqrtx-1)=x-sqrtx+1=7+1=8
8 minutes for a task that takes 10 sec (mentally)...
That's me! 😜😁😂
Evaluating a Radical Expression: x - sqrt(x) = 7; x - 7/sqrt(x) = ?
x - sqrt(x) = 7; x > 7
[x - sqrt(x)]/sqrt(x) = sqrt(x) - 1 = 7/sqrt(x)
x - 7/sqrt(x) = x - sqrt(x) + 1 = 7 + 1 = 8
Oh dear. Divide by sqrtx. Add this equation to the original. Rearrange to give x-7/sqrtx = 8. End.
Method tow. You used the same relationship twice. I find this dangerous as it often gives your result something like 1=1.
Why make it complicated when you can make it simple ? x=7+square(x) , 7/square(x)=square(x)-1 , therefore 7+square(x)-[square(x)-1]= 7+1 . Am I not right ?
Yes
Keep calm, the answer is "?", evertime, in every poor internet equation.
Let S(x) be square root of x.
x - S(x) = 7 (a)
x - 7 = S(x)
Divide by S(x)
S(x) - 7/S(x) = 1 (b)
Add a and b together to get
x - 7/S(x) = 7 + 1 = 8.
No Need to multiply by 14, you could simplify It 😉
that's right
Answer: 8
Answer is 8
That was show!
🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷🇧🇷
8
👍
In general, if we have x - sqrt x = a and we want to find x - a/sqrtx, this is a + 1.
I think that you already have been a video where x = 5. You should remember that ☺️
Sorry, pointless video. Your second solution just begs to be applied from the very beginning and it looks like I'm not the only one who did it. I liked your many other videos but this was just waste.