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Q6.Solve 4x-+ 1 + 410

Answer»

4^(x+1)+4^(1-x)=10

4^x.4+4/4^x=10

4^x+1/4^x=10/4=5/2 , let 4^x=p

p+1/p=5/2

2p^2+2=5p

2p^2 - 5p + 2 =0

2p^2 -4p -p +2=0

2p(p-2)-1(p-2)=0

(p-2)(2p-1)=0

p= 2 , 1/2 , put p= 4^x or 2^2x

2^2x=2 or 2^1

2x=1 => x=1/2 , Answer

2^2x=1/2=2^(-1)

2x=-1 => x=-1/2 , Answer

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