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The sum of the values of x satisfying th...

The sum of the values of `x` satisfying the equation `(31+8sqrt(15))^(x^(2)-3)+1=(32+8sqrt(15))^(x^(2)-3)` is

A

3

B

0

C

2

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
2
`(31 + 8sqrt(15))^(x^(2) - 3) + 1 = (32 + 8sqrt(15))^(x^(2) - 3)`
or `(31 + 8sqrt(15))^(x^(2) - 3) + 1^(x^(2) - 3) = (32 + 8sqrt(15))^(x^(2) - 3)`
`rArr x^(2) - 3 = 1` or `x = pm 2 " " [because a^(n) + b^(n) = (a + b)^(n)]`
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