Test Index

RRB NTPC Mains or Stage 2 Model Paper 3 with solutions

© examsnet.com

Question : 18 of 120

Marks: +1, -0

If

X^4 + \frac{1}{X^4} = 23

then the value of

\left[ X - \frac{1}{X} \right]^2

will be

7
– 7
– 3
3

Solution:

Concept:

Use the identity

\left(a-b\right)^2=a^2+b^2-2ab

and the fact that for real non-zero

x

,

x^2+\frac{1}{x^2}\ge 2

.

Explanation:

Let

y=x^2+\frac{1}{x^2}

.

Then

y^2=x^4+\frac{1}{x^4}+2

.

Given

x^4+\frac{1}{x^4}=23

, so

y^2=23+2=25

.

Since

x

is real,

x^2+\frac{1}{x^2}\ge 2

, hence

y=5

.

Now

\left(x-\frac{1}{x}\right)^2=x^2+\frac{1}{x^2}-2

.

Substitute

x^2+\frac{1}{x^2}=5

.

\left(x-\frac{1}{x}\right)^2=5-2=3

.

Answer:

The value is

3

, so the correct option is D.

© examsnet.com

Go to Question:

Prev Question

Next Question