Question

Chứng minh các phương trình sau vô nghiệm :

a. x² + 3 ( x - 2 )² = 0

b. 2(x + 1)² + ( x + 3 ) = 0

Answer 1

a.

\(x^2+3\left(x-2\right)^2=0\)

\(\Leftrightarrow x^2+3x^2-12x+12=0\)

\(\Leftrightarrow\left(2x\right)^2-2\cdot2x\cdot3+3^2=-3\)

\(\Leftrightarrow\left(2x-3\right)^2=-3\) (vô lí)

Vậy S = {\(\phi\)}

b.

\(2\left(x+1\right)^2+\left(x+3\right)=0\)

\(\Leftrightarrow2x^2+4x+2+x+3=0\)

\(\Leftrightarrow2x^2+5x+5=0\)

\(\Leftrightarrow2\left(x^2+2\cdot x\cdot\dfrac{5}{4}+\dfrac{25}{16}\right)=-\dfrac{15}{8}\)

\(\Leftrightarrow2\left(x+\dfrac{5}{4}\right)^2=-\dfrac{15}{8}\)

Vậy S = {\(\phi\)}