Question

3 to the power x + 2 + 3 to the power minus x equal to 10​

Answer 1

$GOOD \: \: MORNING \: \\ \\ 3 {}^{(x + 2)} + 3 {}^{ - x} = 10 \\ \\ 3 {}^{x} \times 3 {}^{2} + 1 \div (3 {}^{x} ) = 10 \\ \\ put \: \: 3 {}^{x} = z \: \: \: we \: have \: \\ \\ 9z {}^{2} - 10z + 1 = 0 \\ \\ 9z {}^{2} - 9z - z + 1 = 0 \\ \\ 9z(z - 1) - 1(z - 1) = 0 \\ \\ (9z - 1) = 0 \: \: \: or \: \: (z - 1) = 0 \\ \\ z = 1 \div 9 \: \: \: \: or \: \: \: \: z = 1 \\ \\ z = 3 {}^{ - 2} \: \: \: \: or \: \: \: \: z = 1 \\ \\ \\ so \: \: 3 {}^{x} = 3 {}^{ - 2} \: \: \: or \: \: \: 3 {}^{x} = 3 {}^{0} \: \: becoz \: 3 {}^{0} = 1 \\ \\ now \: compare \: powers \: of \: 3 \: we \: have \\ \\ x = - 2 \: \: \: or \: \: x = 0$

Answer 2

X=-2 and x=0

I think it is the correct answer