InterviewSolution
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InterviewSolution
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The number of real solutions of equation `2^(x/2)+(sqrt2+1)^x=(5+2sqrt2)^(x/2)` isA. 1B. 2C. 4D. infinite |
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Answer» Correct Answer - A We have, `2^(x//2)+(sqrt(2)+1)^(x)=(5+2sqrt(2))^(x//2)` `(sqrt(2))^(x)+(sqrt(2)+1)^(x)={sqrt((sqrt(2))^(2)+(sqrt(2)+1)^(2))}^(x)` `implies (sqrt(2))^(x)+(sqrt(2)+1)^(x)=(sqrt(5+2sqrt(2)))^(x)` `implies ((sqrt(2))/(sqrt(5+2sqrt(2))))^(x)+((sqrt(2)+1)/(sqrt(5+2sqrt(2))))^(x)=1` `implies ((sqrt(2))/(sqrt(5+2sqrt(2))))^(x)+((sqrt(2)+1)/(sqrt(5+2sqrt(2))))^(x)=((sqrt(2))/(sqrt(5+2sqrt(2))))^(2)+((sqrt(2)+1)/(sqrt(5+2sqrt(2))))^(x)` `implies x=2` |
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