InterviewSolution
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InterviewSolution
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If `alpha` and `beta` be the roots of equation `x^(2) + 3x + 1 = 0` then the value of `((alpha)/(1 + beta))^(2) + ((beta)/(1 + alpha))^(2)` is equal toA. `18`B. `19`C. `20`D. `21` |
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Answer» Correct Answer - A `(a)` `alpha+beta=-3` , `alpha beta=1`. Also `alpha^(2)+3alpha+1=0` and `beta^(2)+3beta+1=0` `implies` where `alpha^(2)=-(3alpha+1)` and `beta^(2)=-(3beta+1)` `y=(alpha^(2))/((1+beta)^(2))+(beta^(2))/((alpha+1)^(2))` `= (alpha^(2))/(1+2beta+beta^(2))+(beta^(2))/(1+2alpha+alpha^(2))` `=((-(3alpha+1))/(-beta))+((-(1+3beta))/(-alpha))` `=(1+3alpha)/(beta)+(1+3beta)/(alpha)` `=(alpha(1+3alpha)+beta(1+3beta))/(alpha beta)` `=3(alpha^(2)+beta^(2))+(alpha+beta)` (as `alpha beta=1`) `=3[9-2]+(-3)=21-3=18` |
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