(x^2-x-2)(x^2+11x+28)-19用换元法

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(x^2-x-2)(x^2+11x+28)-19用换元法
(x^2-x-2)(x^2+11x+28)-19
用换元法

(x^2-x-2)(x^2+11x+28)-19用换元法
(x^2-15x+54)(x^2+11x+28)+350
=(x-6)(x-9)(x+4)(x+7)+350
=[(x-6)(x+4)][(x-9)(x+7)]+350
=(x^2-2x-24)(x^2-2x-63)+350
设u=x^2-2x,则
(x^2-2x-24)(x^2-2x-63)+350
=(u-24)(u-63)+350
=u^2-87u+1862
=(u-38)(u-49)
=(x^2-2x-38)(x^2-2x-49)
=(x-1+√39)(x-1-√39)(x-1+5√2)(x-1-5√2)

=(x-2)(x+1)(x+4)(x+7)-19
=[(x-2)(x+7)][(x+1)(x+4)]-19
=[(x^2+5x)-14][(x^2+5x)+4]-19
=(x^2+5x)^2-10(x^2+5x)-56-19
=(x^2+5x)^2-10(x^2+5x)-75
=(x^2+5x-15)(x^2+5x+5)