Published by:
CGP EDU Academic Team
Published on: August 13, 2026
Prove that the expression 
– 
+ 
remains unchanged if y is replaced by 
.
Text Solution
Verified by ExpertsThe correct answer is:
CHECK THE SOLUTION.
Sol. Let y 1 = 
. Then,
= 
y ′ . .. (i)
⇒ 
= – 2 
Differentiating both sides with respect to x, we get
– 
= – 2 
... (ii)
Differentiating w.r.t. x, we get
– 
+ 
= – 2 
... (iii)
Using (i), (ii) and (iii) can be written as
– 
= 
– 
... (iv)
– 
+ 
= 
– 
+ 
... (v)
Subtracting 3/2 times the square of (iv) from (v), we get
– 
+ 
= 
– 
+ 
This shows that the given expression does not change if y is replaced by 
.
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