InterviewSolution
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InterviewSolution
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If `x_1, x_2` be the roots of the equation `x^2 -3x+ A=0` and `x_3,x_4` be those of the equation `x^2-12x + B = 0` and `x_1 , x_2, x_3, x_4` be an increasing GP. find find A and B. |
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Answer» `therefore x_(1),x_(2),x_(3),x_(4) " are in GP. "` Let `therefore x_(2)=x_(1)r,x_(3)=x_(1)r^(2),x_(4)=x_(1)r^(3)` `" " [" here, product of " x_(1),x_(2),x_(3),x_(4)" are not given "]` Given, `x_(1)+x_(2)=3,x_(1)x_(2)=A` `implies x_(1)(1+r)=3,x_(1)^(2)r=A " " ".....(i)"` and `x_(3)+x_(4)=12,x_(3)x_(4)=B` `implies x_(1)r^(2)(1+r)=12,x_(1)^(2)r^(5)=B" " ".....(ii)"` from Eqs. (i) and (ii), `r^(2)=4 implies r=2" "[" for increasing GP "]` From Eqs. (i), `x_(1)=1` Now, `A=x_(1)^(2)r=1^(2)*2=2 " " [" from Eq. (i)"]` and `B=x_(1)^(2)r^(5)=1^(2)*2^(5)=32 " " [" from Eq. (ii)"]`. |
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