InterviewSolution
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InterviewSolution
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If `5^x+(2sqrt(3))^(2x)geq1 3^x` then the solution set forA. `[2,oo)`B. {2}C. `(-oo,2]`D. [0,2] |
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Answer» Correct Answer - C We have, `5^(x)+(2sqrt(3))^(2x)ge13^(x)` `implies ((5)/13)^(x)+((12)/(13))^(x)ge1` `implies a^(x) +b^2ge 1`,where `s(5)/(12)` and `b=(12)/(13) ` ` implies a^(x) =b^(x) ge 1 `, where `a^(2) +b^(2) =1` Let `f(x) =a^(x) +b^( x)` we observe that `f(2) = a^(2) + b^(2) =1` Also, `f(x) gt 1` for `x lt 2` and `f(x) lt 1 ` for `x gt 2` Thus, `f(x) ge 1`for `x le 2`. Hence, the solution set of the given inequation is `(-oo,2]`. |
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