InterviewSolution
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InterviewSolution
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Solve the equation `x^(2)+(x/(x-1))^(2)=8` |
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Answer» Correct Answer - `x_(1)=2,x_(2)=-1+sqrt(3)` and `x_(3)=-1-sqrt(3)` We have `x^(2)+(x/(x-1))^(2)=8` `implies(x+x/(x-1))^(2)-2.x.x/((x-1))=8` `implies(x^(2))/(x-1))^(2)-2((x^(2))/(x-1))-8=0`.........i Let `y=(x^(2))/(x-1)`. Then Eq. (i) reduces to `y^(2)-2y-8=0` `implies(y-4)(y+2)=0` `:.y=4,-2` If `y=4` then `4=(x^(2))/(x-1)` or `x^(2)-4x+4=0` or `(x-2)^(2)=0` or `x=2` `:.x_(1)=2` and if `y=-2`, then `-2=(x^(2))/(x-1)` or `x^(2)+2x-2=0` `:.x=(-2+-sqrt((4+8)))/2` `impliesx=-1+-sqrt(3)` `:.x_(2)=-1+sqrt(3),x_(3)=-1-sqrt(3)` |
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