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the roots of the equation (a+sqrt(b))^(x...

the roots of the equation `(a+sqrt(b))^(x^2-15)+(a-sqrt(b))^(x^2-15)=2a` where `a^2-b=1` are

A

`pm 4`

B

`pm3`

C

`pm sqrt(14)`

D

`pm sqrt (5)`

Text Solution

Verified by Experts

The correct Answer is:
1,3
We have `(a + sqrt(b))^(x^(2) - 15) + (1)/((a + sqrt(b))^(x^(2) - 15))= 2a`
` y^(2) - 2ay + 1 = 0 `, where ` y = (a + sqrt(b))^(x^(2) - 15)`
`therefore y = a pm sqrt(a^(2) - 1) = apm sqrt(b) = (a + sqrt(b))^(x^(2) - 15)`
So, ` x^(2) - 15 = pm 1`
`therefore x = pm 4, sqrt(14)` .
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