Please solve the below problem:If y=x^1/3-x^-1/3, then y^3+3y=?
Prasant Sahu , 6 Years ago
Grade 12th pass
Algebra> Please solve the below problem: If y=x^1/...
1 Answers
Snehal Jadhav
Last Activity: 6 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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