Question Details

If x4 + 1x4 = 322, x ≠ 0, then one of the values of (x − 1x) is

Options

A

2

B

4

C

6

D

8

Show Answer

Correct Answer :

Option B

4

Solution :

The correct answer is Option 4.

We are given the equation:

x4+1x4=322

We need to find one of the values of (x − 1x).

First, recall the algebraic identity:

x2+1x22=x4+1x4+2

Substitute the given value of x4+1x4=322 into the identity:

x2+1x22=322+2=324

Taking the square root on both sides (since x2+1x2>0 for real x ≠ 0):

x2+1x2=324=18

Next, use the identity for (x − 1x)2:

x-1x2=x2+1x2-2

Substitute x2+1x2=18 into the equation:

x-1x2=18-2=16

Taking the square root on both sides:

x-1x=±4

Thus, one of the values of (x − 1x) is 4.

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