3^(x+2) +3^-x =10 solve for x

.Q.  3^(x+2) +3^-x =10 solve for x

ANS :  3^(x+2) +3^-x =10

=> 3^x 3²  + (1 / 3^x) = 10

=> 9 * 3^x   + (1 / 3^x) = 10

Let  y = 3^x 

Therefore : 9 * y   + (1 / y) = 10

(9y ² + 1) = 10 y

So :  9y ² -10 y + 1 = 0

Applying Splitting the middle term method  : 9 = (-9) * (-1)

=> 9y ² +(-10 y) + 1 = 0

=> 9y ² +(-9 y - y) + 1 = 0

So : 9y ( y-1) - 1 ( y-1) = 0

=> (9y-1) (y-1) = 0

Now : (9y-1) =0  or  (y-1) = 0

Therefore :  y = (1 / 9)  or  y = 1

Since : y = 3^x 

So : 3^x = (1 / 9)  or  3^x = 1

3^x = (3 ²)^-1  or  3^x = (3)⁰

Therefore :  3^x = (3 ^-2)  or  3^x = (3)⁰

Comparing the both sides :  x = -2  or  x  = 0

The value of x :  -2  or  0

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