solve (15-4√14)^t +(15+4√14)^t=30 ;where t= (x^2)- 2x

Question

find solution of (15-4√14)^t +(15+4√14)^t=30 ;where t= (x^2)- 2x

Answer 1

find solution of (15-4√14)^t +(15+4√14)^t=30 ;where t= (x^2)- 2x

By observation, puting t = 1 makes the radicals cancel out and the 2 15's add up to 30. So t = 1 is a solution.

t = x^2 - 2x, so x^2 - 2x = 1

x^2 - 2x + 1 - 1 = 1

(x - 1)^2 = 2

x = 1 +/- rt(2)