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Please solve the below problem: If y=x^1/3-x^-1/3, then y^3+3y=?

Please solve the below problem:
If y=x^1/3-x^-1/3, then y^3+3y=?

Grade:12th pass

1 Answers

Snehal Jadhav
54 Points
5 years ago
We are given that:
y=x1/3 – x-1/3
 
The expression asked to solve can be rearranged into:
y2 (y + 3)
 
So, first we will evaluate the value of y2:
Therefore, by squaring on both the sides we get:
 
y2 = (x1/3 – x-1/3)2
    = x2/3 + x-2/3 – 2
 
Now, by inserting the value we get:
= y (x2/3 + x-2/3 – 2 + 3)
= (x1/3 – x-1/3 )(x2/3 + x-2/3 + 1)
= x + x-1/3 + x1/3 –  x1/3 – 1/x –  x-1/3
 
By, cancelling terms we get our final expression:
= x – 1/x

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