Question

7 to the power 1 + X plus 7 to the power 1 - X = 50

Answer 1

${7}^{1 + x} + {7}^{1 - x} = 50 \\ (1 + x)(1 - x) = 50 \\ {1 }^{2} - {x}^{2} = 50 \\ - {x}^{2} = 50 - 1 \\ - {x}^{2} = \sqrt{49} \\ x = + 7 \: or \: - 7$

Answer 2

7^(x+1)+7^(x-1)=50
7^(x+1)+7^(x-1)=49+1=7^2+7^0
comparing LHS=RHS we have
x+1=2 & x-1=0
x=1 & x=1