Question

a)   (x-1) (x^2+x+1)= -9

b)   (12x-5) (4x-1) + (3x-7) ( 1-16x) = 81

Answer 1

a/ \(\left(x-1\right)\left(x^2+x+1\right)=-9\)

=> \(x^2\left(x-1\right)+x\left(x-1\right)+\left(x-1\right)=-9\)

=> \(x^3-x^2+x^2-x+x-1=-9\)

=> \(x^3+\left(x^2-x^2\right)+\left(x-x\right)-1=-9\)

=> \(x^3-1=-9\)

=> \(x^3=-8\)

=> \(x=-2\)

b/ \(\left(12x-5\right)\left(4x-1\right)+\left(3x-7\right)\left(1-16x\right)=81\)

=> \(48x^2-12x-20x+5+3x-48x^2-7+112x=81\)

=> \(\left(48x^2-48x^2\right)+\left(112x-12x-20x+3x\right)+\left(5-7\right)=81\)

=> \(83x-2=81\)

=> \(83x=83\)

=> x = 1