Question

Tìm x, biết:

a) 6(x + 2)(x - 3) - 3(x - 2)² - 3(x - 1)(x + 1) = 1

b) (x - 1)(x² + x + 1) + x(x + 2)(2 - x) = 5

c) (x - 1)³ - (x + 3)(x³ - 3x + 9) + 3(x - 2)(2 + x) = 2

Answer 1

\(a)6\left(x+2\right)\left(x-3\right)-3\left(x-2\right)^2-3\left(x-1\right)\left(x+1\right)=1\\ \Leftrightarrow\left(6x+12\right)\left(x-3\right)-3\left(x^2-4x+4\right)-3\left(x^2-1\right)=1\\ \Leftrightarrow6x^2-18x+12x-36-3x^2+12x-12-3x^2+3=1\\ \Leftrightarrow6x-45=1\\ \Leftrightarrow6x=1+45\\ \Leftrightarrow6x=46\)

\(\Leftrightarrow\)\(x=\dfrac{23}{3}\)

Answer 2

\(b)\left(x-1\right)\left(x^2+x+1\right)+x\left(x+2\right)\left(2-x\right)=5\\ \Leftrightarrow x^3-1+x\left(4-x^2\right)=5\\ \Leftrightarrow x^3-1+4x-x^3=5\\ \Leftrightarrow4x=5+1\\ \Leftrightarrow4x=6\)

\(\Leftrightarrow\)\(x=\dfrac{3}{2}\)