Question

Giải phương trình sau : (x - 1)² + (x + 3)² = 2(x - 2)(x + 1) + 38

Ai hâm mộ Naryto kb

Answer 1

Ta có : (x - 1)² + (x + 3)² = 2(x - 2)(x + 1) + 38

<=> x² - 2x + 1 + x² + 6x + 9 = 2x² - 2x - 4 + 38

<=> x² - 2x + 1 + x² + 6x + 9 - 2x² + 2x + 4 - 14 = 24

<=> x² + x² - 2x² - 2x + 2x + 6x + 1 + 9 + 4 - 14 = 24

<=> 6x = 24

=> x = 24 : 6

=> x = 4 

Answer 2

\(\left(x-1\right)^2+\left(x+3\right)^2=2\left(x-2\right)\left(x+1\right)+38\)

\(\Leftrightarrow\left(x^2-2x+1\right)+\left(x^2+6x+9\right)=2\left(x^2-x-2\right)+38\)

\(\Leftrightarrow2x^2+4x+10=2x^2-2x+34\)

\(\Leftrightarrow2x^2+4x-2x^2+2x=34-10\)

\(\Leftrightarrow6x=24\)

\(\Rightarrow x=4\)