Question
If x, y, z are the three factors of a 3–
7a – 6, then value of x + y + z will beSolution
a3– 7a – 6 ⇒ a3 – a – 6a – 6 ⇒ a(a2 – 1) – 6 (a +1) ⇒ a (a + 1) (a – 1) – 6 (a +1) ⇒ (a +1) [a (a – 1) – 6)] ⇒ (a +1) [a2 – a – 6] ⇒ (a +1) [a2 – 3a + 2a – 6] ⇒ (a +1) [a (a – 3) + 2 (a – 3)] ⇒ (a +1) (a – 3) (a + 2) Let x = (a +1), y = (a – 3) and z = (a + 2) ∴ x + y + z = a + 1 + a – 3 + a + 2 = 3a
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