Question

4. Find the H.C.F and L.C.M of:
i) x^2 - 25, x^2 - 6x + 5 and (x - 5)^2
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Answer 1

$\\ \: \: {x}^{2} - 25 = {x}^{2} - {5}^{2} \\ \\ \: = (x + 5)(x - 5) .......1\\ \\ now \\ {x}^{2} - 6x + 5 = 0 \\ \\ {x}^{2} - 5x - x + 5 = 0 \\ \\ x(x - 5) - 1(x - 5) = 0 \\ \\ (x - 5)(x - 1) = 0.........2 \\ \\ now \\ {(x - 5)}^{2} = (x - 5)(x - 5)........3 \\ \\ from \: \: \: 1.2.3 \\ \\ hcf = (x - 5) \\ \\ lcm = (x - 5)(x - 5)(x - 1)(x + 5)$

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