If(3x^(2) +5x-2)^(2n-1) = 1, find the value of n

Question

If
`(3x^(2) +5x-2)^(2n-1)` = 1, find the value of n

Answer 1

n = 1/2

Explanation:

Assuming that 3x² + 5x - 2 is not zero, and that we can represent 3x² + 5x - 2 with the letter d, then:

d^(2n - 1) = 1. The exponent (2n - 1) of d must be 0 for d^(2n - 1) = 1 to be true. Then 2n - 1 = 0, and 2n = 1, and n = 1/2.

Answer 2

Either
`3x^2+5x-2=1`, in which case
`n` can be anything, or
`3x^2+5x-2\\eq0` and
`2n-1=0`, in which case
`n=\frac12`.