From a non math guy, I’d challenge this solution. The question read “simplify.” You did many things but, simplify is not a descriptor I would choose. 🤣 finding the square root 5, subtracting 2 and finding the cube root of the result….0.618 is simple. But that’s just me…
It is a useful simplification because it is an exact answer that doesn't have nested roots. It's much simpler to work with a number expressed as a + b sqrt(n) where a, b are rational and n is a natural number, than with the original expression. Your answer is a rational approximation of an irrational number, so it loses information.
This question relates to the reciprocal of the golden ratio. It is constructed so that it simplifies. The presence of Fibonacci numbers 2,3,5 might be a clue to the cognisant. But within complex numbers there would be two real values and four more complex values.
^=read as to the power *=read as square root As per question (*5-2)^(1/3) Let's explain *5 - 2 =8(*5-2)/8 ={8.*5 - 16)/8 ={(5.*5)+(3.*5)-15-1}/8 ={(5.*5)-1-15+(3.*5)}/8 =[(*5)^3 - (1^3)-{3×(*5)^2×1}+{3×*5×(1^2)}]/8 ={(*5-1)^3}/(2^3) ={(*5-1)/2}^3 As per question [{(*5-1)/2}^3]^(1/3) =(*5-1)/2
What has made your channel and videos get such great views and become so popular? I watched a lot of your videos and you’re perfect in math and explain 👌🏻👌🏻👌🏻
Because the original expression approximates to a positive value and only a positive value. If your simplification includes a negative then you did something wrong.
Sorry I’m new to maths but as someone who easily played pool using maths I feel like a lot of explanations are so over the top it’s jarring isn’t the answer 0 or at least very very close to it. I haven’t seen the end of the video I would explain my reasoning but it’s so inherent that it’s hard to care if I have energy I will explain it
Interesting. But this is, of coarse, not a higher math. There enouth the knowledge of middle school to solve that, but as a task with higher complexity. Thnx!
Could you please stop explaining the 3 quadratic formulas every time you use them. You call your channel Higher Mathematics and then you should assume that people watching definitely know them already.
Excellent. Thank You
This is brilliant
From a non math guy, I’d challenge this solution. The question read “simplify.” You did many things but, simplify is not a descriptor I would choose. 🤣 finding the square root 5, subtracting 2 and finding the cube root of the result….0.618 is simple. But that’s just me…
It is a useful simplification because it is an exact answer that doesn't have nested roots. It's much simpler to work with a number expressed as a + b sqrt(n) where a, b are rational and n is a natural number, than with the original expression. Your answer is a rational approximation of an irrational number, so it loses information.
This question relates to the reciprocal of the golden ratio. It is constructed so that it simplifies. The presence of Fibonacci numbers 2,3,5 might be a clue to the cognisant.
But within complex numbers there would be two real values and four more complex values.
^=read as to the power
*=read as square root
As per question
(*5-2)^(1/3)
Let's explain
*5 - 2
=8(*5-2)/8
={8.*5 - 16)/8
={(5.*5)+(3.*5)-15-1}/8
={(5.*5)-1-15+(3.*5)}/8
=[(*5)^3 - (1^3)-{3×(*5)^2×1}+{3×*5×(1^2)}]/8
={(*5-1)^3}/(2^3)
={(*5-1)/2}^3
As per question
[{(*5-1)/2}^3]^(1/3)
=(*5-1)/2
That was truly brilliant.
(5^1/2-2)^1/3=a5^1/2-a
5^1/2-2=(a51/2-a)^3=(8a^3)5^1/2-16a^3 then 8a^3=1 and -16a^3=-2
result. a=1/2
answer 1/25^1/2-1/2
What has made your channel and videos get such great views and become so popular?
I watched a lot of your videos and you’re perfect in math and explain 👌🏻👌🏻👌🏻
Why reject negative solutions?
A Negative cube root of a negative number is perfectly reasonable.
I believe negative solutions are rejected because sqrt(5) - 2 is a positive number, therefore cbrt((sqrt(5))-2) will be positive.
answer is greater than 0 , -1-root5/2 is negative
Because the original expression approximates to a positive value and only a positive value. If your simplification includes a negative then you did something wrong.
1) He said in the beginning that cbrt(sqrt(5)-2) is greater than 0
2) If you simplify a number you can't get 2 different values it makes no sense
For an easy reference, what is the name of this method? How can I find it or refer to it?
S. Ferro-N. Tartaglia-J. Cardano's method.
at 10.49 why not 3t ?
x^3 25 ➖ (3)^2=x^3{ 25 ➖ 9}={x^3* 16}=16x^3 2^4x^3 2^2^2x^3 1^1^2x^3 2x^3 (x ➖ 3x+2).
Sorry I’m new to maths but as someone who easily played pool using maths I feel like a lot of explanations are so over the top it’s jarring isn’t the answer 0 or at least very very close to it. I haven’t seen the end of the video I would explain my reasoning but it’s so inherent that it’s hard to care if I have energy I will explain it
Thank you 👌🏻👌🏻👌🏻👌🏻
0,5V5-0,5.
Tks...
Thanks
Engineer says 0.62
Interesting. But this is, of coarse, not a higher math. There enouth the knowledge of middle school to solve that, but as a task with higher complexity.
Thnx!
th th th th th :D
Could you please stop explaining the 3 quadratic formulas every time you use them. You call your channel Higher Mathematics and then you should assume that people watching definitely know them already.