If a + (1/a) = 2, then find the value of (a5 + a3 + 6)/(7a – 5).
Given, a + (1/a) = 2 Or, a2 + 1 = 2a Or, a2 – 2a + 1 = 0 Or, a2 – a – a + 1 = 0 Or, a(a – 1) – 1(a – 1) = 0 Or, (a – 1)(a – 1) = 0 Or, a = 1 So, (a5 + a3 + 6)/(7a – 5) = (1 + 1 + 6)/(7 – 5) = 8/2 = 4
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