Question

7tothe power x+1 + 7 tothe power 1-x = 126

Answer 1

Given, $7^{(x+1)}+7^{(1-x)}=126$

7^(x + 1) + 7^(1 - x) = 126

or, 7^(1 - x)[ 7^2x + 1 ] = 7 × 18

or, 7 × 7 ^-x [ (7²)^x + 1 ] = 7 × 18

or, (7^x)² + 1 = 18.7^x

Let 7^x = P

or, P² + 1 = 18P

or, P² - 18P + 1 = 0

P = {18 ± √(324 - 4)}/2

P = {18 ± √(300)}/2

7^x = 9 ± 5√3

taking log both sides,

xlog7 = log(9 ± 5√3)

x = log(9 ± 5√3)/log7

hence x = log(9 + 5√3)/log7 , log(9 - 5√3)/log7