InterviewSolution
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InterviewSolution
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If `m`, `n` are positive integers and `m+nsqrt(2)=sqrt(41+24sqrt(2))`, then `(m+n)` is equal toA. `5`B. `6`C. `7`D. `8` |
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Answer» Correct Answer - C `(c )` We have `m+nsqrt(2)=sqrt(41+24sqrt(2))` Squaring both sides, we get `m^(2)+2n^(2)+2sqrt(2)mn=4a+24sqrt(2)` `:.` On comparing we get `m^(2)+2n^(2)=41`…….`(i)` and `mn=12`…….`(ii)` `:.` On solving `(i)` and `(ii)`, we get `implies m^(2)+(2(144))/(m^(2))=41` `impliesm^(4)=41m^(2)+288=0` `implies (m^(2)-32)(m^(2)-9)=0` `implies m^(2) ne 32` `:. m^(2) =9 implies m =3` and `n=4` Hence, `(m+n)=7` |
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