Question-174303

Question Number 174303 by dragan91 last updated on 29/Jul/22

Answered by a.lgnaoui last updated on 29/Jul/22

x^{2} - 10 x - a x + 10 a + 1 = x^{2} + c x + b x + b c

x^{2} - (10 + a) x + 10 a + 1 = x^{2} + (b + c) x + b c

- (10 + a) = b + c

10 a + 1 = b c

b, c v e r i f i e l e q u a t i o n :

z^{2} - (10 + a) z + 10 a + 1 = 0

Δ = {(10 + a)}^{2} - 4 (10 a + 1)

= a^{2} - 20 a + 96 = (a - 12) (a - 8)

∙ a = 8

b + c = - 18 b c = 81

z^{2} + 18 z + 81 = {(z + 9)}^{2}

d o n c a = 8; b = c = - 9

∙ a = 12

b + c = - 22 b c = 121

z^{2} + 22 z + 121 = {(z + 11)}^{2}

d o n c a = 12; b = c = - 11

Commented by Tawa11 last updated on 29/Jul/22

Great sir

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