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InterviewSolution
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Solve the following quadratic equations by factorization:\((a+b)^{2}x^{2}-4abx-(a-b)^{2}=0\) |
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Answer» In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized. \((a+b)^{2}x^{2}-4abx-(a-b)^{2}=0\) ⇒ (a + b)2x2 - (a2 + b2 + 2ab – a2 – b2 + 2ab)x – (a – b)2 = 0 ⇒ (a + b)2x2 – (a + b)2x + (a – b)2x – (a – b)2 = 0 ⇒ (a + b)2x(x - 1) + (a – b)2(x – 1) = 0 ⇒ ((a + b)2x + (a – b)2)(x – 1) = 0 ⇒ x = 1, \(-\frac{(a-b)^{2}}{(a+b)^{2}}\) |
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