Question

solve the equation and find the value of x : 3^x + 3^-x =2​

Answer 1

Step-by-step explanation:

${3}^{x} + {3}^{-x} = 2 \\</p><p> {3}^{x} + \frac{1}{{3}^{x}} = 2 \\</p><p> \frac{{3}^{2x} +1}{{3}^{x} } =2 \\</p><p> {3}^{2x} +1=2 \times {3}^{x} \\ ({3}^{x})^{2} - 2 \times {3}^{x} + 1 = 0 \\( {3}^{x} - 1)^{2} = 0 \\ {3}^{x} - 1 = 0 \\ {3}^{x} = 1 \\ {3}^{x} = {3}^{0}... (\because {3}^{0}=1)\\ \implies x = 0$