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InterviewSolution
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Solve the following quadratic equations by factorization:Solve for x: \(\frac{x-1}{x-2}+\frac{x-3}{x-4}=3\frac{1}{3},x\neq2,4\) |
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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. \(\frac{x-1}{x-2}+\frac{x-3}{x-4}=3\frac{1}{3},x\neq2,4\) ⇒ 3(x– 1)(x – 4) + 3(x – 2)(x – 3) = 10(x – 2)(x – 4) ⇒ 3x2 + 12 – 15x + 3x2 + 18 – 15x = 10x2 – 60x + 80 ⇒ 4x2 – 30x + 50 = 0 ⇒ 2x2 – 15x + 25 = 0 ⇒ 2x2 – 10x – 5x + 25 = 0 ⇒ 2x(x – 5) – 5(x – 5) = 0 ⇒ (2x – 5)(x – 5) = 0 Thus, x = 5/2, 5 |
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