Solve {c}{y=2x_1^2+4x_2^2+x_{1}x_{2}}{x_{1}=9/4}{x_{2}=-9/32}

$$\left. \begin{array} { c } { y = 2 x _ { 1 } ^ { 2 } + 4 x _ { 2 } ^ { 2 } + x _ { 1 } x _ { 2 } } \\ { x _ { 1 } = \frac { 9 } { 4 } } \\ { x _ { 2 } = - \frac { 9 } { 32 } } \end{array} \right.$$

Solve for y, x_1, x_2

$$y = \frac{2511}{256} = 9\frac{207}{256} = 9.80859375$$

$$x_{1} = \frac{9}{4} = 2\frac{1}{4} = 2.25$$

$$x_{2}=-\frac{9}{32}=-0.28125$$

Solution Steps

Consider the first equation. Insert the known values of variables into the equation.

$$y=2\times \left(\frac{9}{4}\right)^{2}+4\left(-\frac{9}{32}\right)^{2}+\frac{9}{4}\left(-\frac{9}{32}\right)$$

Calculate \frac{9}{4} to the power of 2 and get \frac{81}{16}.

$$y=2\times \frac{81}{16}+4\left(-\frac{9}{32}\right)^{2}+\frac{9}{4}\left(-\frac{9}{32}\right)$$

Multiply 2 and \frac{81}{16} to get \frac{81}{8}.

$$y=\frac{81}{8}+4\left(-\frac{9}{32}\right)^{2}+\frac{9}{4}\left(-\frac{9}{32}\right)$$

Calculate -\frac{9}{32} to the power of 2 and get \frac{81}{1024}.

$$y=\frac{81}{8}+4\times \frac{81}{1024}+\frac{9}{4}\left(-\frac{9}{32}\right)$$

Multiply 4 and \frac{81}{1024} to get \frac{81}{256}.

$$y=\frac{81}{8}+\frac{81}{256}+\frac{9}{4}\left(-\frac{9}{32}\right)$$

Add \frac{81}{8} and \frac{81}{256} to get \frac{2673}{256}.

$$y=\frac{2673}{256}+\frac{9}{4}\left(-\frac{9}{32}\right)$$

Multiply \frac{9}{4} and -\frac{9}{32} to get -\frac{81}{128}.

$$y=\frac{2673}{256}-\frac{81}{128}$$

Subtract \frac{81}{128} from \frac{2673}{256} to get \frac{2511}{256}.

$$y=\frac{2511}{256}$$

The system is now solved.

$$y=\frac{2511}{256} x_{1}=\frac{9}{4} x_{2}=-\frac{9}{32}$$