Question

The number of real solutions of the equation `( 15 + 4sqrt14 )^t + (15 - 4sqrt14)^t = 30` are where `t=x^2-2|x|`?

Answer 1

See below.

Explanation:

For `t = 1` we have

`( 15 + 4sqrt14 )^1 + (15 - 4sqrt14)^1 = 30`

Now we left as an exercise the solution for

`1=x^2-2|x| hArr 1=absx^2-2absx hArr absx^2-2absx-1=0`