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

Options

A. `pm 4`
B. `pm3`
C. `pm sqrt(14)`
D. `pm sqrt (5)`

Answer

1,3

Explanation

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)` .