InterviewSolution
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InterviewSolution
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Find he linear factors of `2x^2-y^2-x+x y+2y-1.` |
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Answer» Given expression is `2x^(2) - y^(2) - x + xy + 2y -1` (1) Its corresponding equation is `2x^(2) - y^(2) - x +xy + 2y - 1 = 0` or `2x^(2)-(1 -y)x - (y^(2) - 2y + 1) = 0` `therefore x = (1-y pm sqrt((1-y)^(2) + 4.2(y^(2)-2y + 1)))/(4)` `= (1-y pm sqrt((1-y)^(2) + 8(y-1)^(2)))/(4)` `= (1-y pm sqrt(9(1-y^(2))))/(4)` `= (1-y pm 3(1-y))/(4)` `1 - y, - (1 -y)/(2)` Hence, the required factors are (x + y -1) and (2x - y + 1). |
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