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Question
`3^((x+2))+3^(-x)=10`
Solution
`3^((x+2))+3^(-x)=10`
`3^(x)9+1/3^(x)=10`
Let `3^x` be equal to y.
∴` 9y+1/y=10`
⇒`9y^2+10y+1=0`
⇒`9y^2-10y+1=0`
⇒`(y-1) (9y-1)=0`
⇒`y=1 or y=1/9`
⇒`3x^x=1 or 3^x=1/9`
⇒`3^x=3^0 or 3^x=3^-2`
⇒`x=0 or x=-2`
Hence, 0 and -2 are the roots of the given equation.
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