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Example - 5. Solve 3^{x + 2} + 3 ^{- x} = 10

Solution : 3^{x + 2} + 3 ^{- x} = 10

Or, 3^x . 3² + 3 ^{- x} = 10

Or, 9.3^x + 1/3^x = 10

Put 3^x = y

Or, 9y² + 1 = 10y

Or, 9y² - 10y + 1 = 0

Or, 9y² - 9y - y + 1 = 0

Or, 9y(y - 1) -1 (y - 1) = 0

Or, (y - 1) (9y - 1) = 0

When y = 1 ; 3^x = 1 = 3⁰

When y = 1/9 ; 3^x = 1/9

= 1/3² = 3^-2

Ans. x = 0, - 2