Question

Chi pt x(3x-4)=2x2 +1 A= x1 mu 2 + x2 mu 2 +3x1x2 Giup mk nha

Answer 1

\(x\left(3x-4\right)=2x^2+1\)

\(\Leftrightarrow3x^2-4x-2x^2-1=0\)

\(\Leftrightarrow x^2-4x-1=0\)

Theo Vi - ét, ta có :

\(\left\{{}\begin{matrix}x_1+x_2=-\dfrac{b}{a}=4\\x_1x_2=\dfrac{c}{a}=-1\end{matrix}\right.\)

Ta có :

\(A=x_1^2+x_2^2+3x_1x_2\)

\(=\left(x_1+x_2\right)^2-2x_1x_2+3x_1x_2\)

\(=\left(x_1+x_2\right)^2+x_1x_2\)

\(=4^2-1\)

\(=16-1\)

\(=15\)