Question

(х+4)(х+6)(х+8)(х+10)=9

Answer 1

$(x+4)(x+10)(x+8)(x+6)=9 \ (x^2+10x+4x+40)(x^2+6x+8x+48)=9 \ (x^2+14x+40)(x^2+14x+48)=9$
замена
$x^2+14x=a \ (a+40)(a+48)=9 \ a^2+48a+40a+1920=9 \ a^2+88a+1911=0 \ D=7744-7644=100 =10^2 \ a_1= frac{-88-10}{2}=-49 \ a_2= frac{-88+10}{2}= -39 \ \ x^2+14x=-39 \ x^2+14x+39=0 \ D=196-144=52=(2 sqrt{13})^2 \ x_1= frac{-14-2 sqrt{13} }{2}(:2)=-7- sqrt{13} \ x_2= -7 + sqrt{13} \ \ x^2+14x=-49 \ x^2+14x+49=0 \ (x+7)^2=0 \ x_3=-7$

Answer 2

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