Question

Tìm x biết:

a) (x-1)(x^2+x+1) - x(x+2)(x-2) = 5

b) (6x-2)^2 + (5x-2)^2 - 4(3x-1)(5x-2) = 0

c) (x+1)^3 - x(x-2)^2 + x - 1 = 0

Answer 1

a. \(\left(x-1\right)\left(x^2+x+1\right)-x\left(x+2\right)\left(x-2\right)=5\Leftrightarrow x^3-1-x\left(x^2-4\right)=5\Leftrightarrow x^3-1-x^3+4x=5\Leftrightarrow4x-1=5\Leftrightarrow4x=6\Leftrightarrow x=\dfrac{3}{2}\)

b. \(\left(6x-2\right)^2+\left(5x-2\right)^2-4\left(3x-1\right)\left(5x-2\right)=0\Leftrightarrow36x^2-24x+4+25x^2-20x+4-4\left(15x^2-6x-5x+2\right)=0\Leftrightarrow36x^2-24x+4+25x^2-20x+4-60x^2+24x+20x-8=0\Leftrightarrow x^2=0\Leftrightarrow x=0\)

c. \(\left(x+1\right)^3-x\left(x-2\right)^2+x-1=0\Leftrightarrow x^3+3x^2+3x+1-x\left(x^2-4x+4\right)+x-1=0\Leftrightarrow x^3+3x^2+3x+1-x^3+4x^2-4x+x-1=0\Leftrightarrow7x^2=0\Leftrightarrow x=0\)