Japanese | A Nice Radical Problem | Find the Value of x

[@BrijLalSahu-bb1lu]

🎉🎉 very nice @MATHS TUTORIAL ( BL SAHU)

[@raghvendrasingh1289]

Putting cube root 3 = y , multiplying numerator and denominator by (y - 1) we get 2x = y^2 - y where y^3 = 3
cubing both sides
8 x^3 = y^6 - y^3 - 3 y^3(y^2-y)
8 x^3 = 6 - 9(2x)
8 x^3+18 x= 6
4 x^3+9 x = 3
ans = 4/5

[@ArwindSah]

Q. 4
X^4 -X^2 = -1 find X
X^4 -X^2 + 1=0
(X^2+1)^2 - 3X^2 =0
(X^2+1)^2 - √3 X^2=0
(X^2+1+√3 X)(X^2+1-√3 X) =0
Hence
X^2+√3 X + 1 =0
Or X^2 - √3 X +1 =0
We have two quadratic equation. Hope you can solve them
Q. 3
(X^2 -3X)^2 -(X^2 - 3X)=20. Find X
Let t = X^2 - 3X
Then t^2 - 8t = 20
t^2 - 8 t -20 = 0
t^2 -10t + 2t - 20 =0
t(t-10) + 2(t,-10)=0
(t-10)(t+2) =0
Hence t-10 =0 or t+2=0
t=10 or t= -2
Recall t
We get two equation X^2 - 3X =10
And X^2 -3X = -2
Hope you can solve them
Q.2
25X^2 + 49 Y^2 = 841
XY=12
find X, Y
Solution
Since
25X^2 + 49 Y^2 can be written as
(5X+7Y)^2- 2.5X.7Y
Or
(5X - 7Y)^2 + 2.5X.7Y
Putting the value of XY We get
5X+7Y= √(841+840)=√1681 =41
And 5X - 7Y =√(841-840) = √1=1
Solving these two equation you get value of X and Y.
X=21/5. Y= 20/7
Q.1
a - b = 2. Eq. 1
a^5 - b^5 = 992. Eq.2
a= ? b =?
Solution
(a - b)^3 = a^3 -b^3 -3ab(a-b)
Or
a^3 - b^3 = 2^3 - 3ab.2 a^3 - b^3 = 8+🎉🎉6ab... Eq.3
(a-b)^5 = a^5 -b^5 -5a^4b+10a^3b^2-10a^2b^3+5ab^4
Then
2^5 = 992 -5ab(a^3-2a^2 +2ab^2 - b^3) = 992 -5ab{(a^3 -b^3) - 2ab(a-b)}
Use eq.3 and 1
32=992- 5ab{(8+6ab)-4ab}
Or 32 = 992 - 40ab -10(ab)^2
Or
10(ab)^2+40ab-960 =0
=(ab)^2 + 4ab -96 = 0
Solving this eq. You get
Value of ab = 8 or - 12
Now we have two cases
Case 1. Case 2
a - b = 2. a - b =2
ab = 8. ab = -12
Hope you know how to solve them
Thanks

[@VICKEYKUMAR-e3s]

Your Video was very helpful and very nice for education.
But I have a problem in some questions and I am trying hard to hard but not able to find exact answers of variables. Can you solve those for me ?
Q. 1 Given -
a - b = 2 , a^5 - b^5 = 992
a = ? , b = ?
Q. 2. Given -
25x^2 + 49y^2 = 841 ,
xy = 12 , x = ? , y = ?
Q. 3. Given -
(x^2 - 3x)^2 - 8(x^2 - 3x) = 20 , x = ?
Q. 4. Given -
x^4 - x^2 = -1 , x = ?
Please , Solve these questions and help me . Solve when ( or if ) you are free .