Question

Tìm x, biết:

a) \(5x\left(x-3\right)^2-5\left(x-1\right)^3+15\left(x+2\right)\left(x-2\right)=5\)

b) \(\left(x+2\right)\left(3-4x\right)=x^2+4x+4\)

Answer 1

a) 5x ( x - 3 )² - 5 ( x - 1 )³ + 15 ( x + 2 )( x - 2) = 5

⇔ x ( x - 3 )² - ( x - 1 )³ + 3 ( x + 2 ) ( x - 2 ) = 1

⇔ x (x² - 6x + 9) - (x³ - 3x² + 3x - 1) + 3(x² - 4) = 1

⇔ x³ - 6x² + 9x - x³ + 3x² - 3x + 1 + 3x² - 12 = 1

⇔ 6x - 11 = 1 ⇔ 6x = 12 ⇔ x = 2

b) ( x + 2 ) ( 3 - 4x ) = x² + 4x + 4

⇔ ( x + 2 ) ( 3 - 4x ) = ( x + 2 )²

⇔ 3 - 4x = x + 2 ⇔ 5x = 1

⇔ x = 1/5

Answer 2

b) \(\left(x+2\right).\left(3-4x\right)=x^2+4x+4\)

\(\Rightarrow\left(x+2\right).\left(3-4x\right)=x^2+2.x.2+2^2\)

\(\Rightarrow\left(x+2\right).\left(3-4x\right)=\left(x+2\right)^2\)

\(\Rightarrow\left(3-4x\right)=\left(x+2\right)^2:\left(x+2\right)\)

\(\Rightarrow3-4x=x+2\)

\(\Rightarrow3-2=x+4x\)

\(\Rightarrow1=5x\)

\(\Rightarrow x=1:5\)

\(\Rightarrow x=\frac{1}{5}\)

Vậy \(x=\frac{1}{5}.\)

Chúc bạn học tốt!