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Question
`4^((x+1))+4^((1-x))=10`
Solution
`4^((x+1))+4^((1-x))=10`
⇒ `4^(x + 1) + 4 · 4^x, 4^(1 - x) = 4/(4^x)`
⇒ `4 · 4^x + 4/(4^x) = 10`
Let `4x` be y.
∴ `4y+4/y=10`
⇒`4y^2-10y+4=0`
⇒`4y^2-8y-2y+4=0`
⇒`4y(y-2)-2(y-2)=0`
⇒`y=2 or y=2/4=1/2`
⇒ `4^x=2 or 1/2`
⇒`4^x=2^2x=2^1 or 2^(2x)=2^-1`
⇒`x=1/2` or `x= -(1)/2`
Hence, `1/2` and `-(1)/2` are roots of the given equation.
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