Question

Solve this
Q.30 If x + y - z = 4, $x^2+y^2+z^2=30$, then find the value of xy - yz - zx

Answer 1

$$\begin{gathered} Given \\ 1.x+y-z=4 \\ 2.x^2+y^2+z^2=30 \\ Squaring1. \\ {\left(x+y-z\right)}^2=16 \\ (x+y{)}^2+z^2-2(x+y)z=16 \\ {x}^2+y^2+2xy+z^2-2xz-2yz=16 \\ {\mathit{x}}^{\mathbf{2}}\mathbf{+}{\mathit{y}}^{\mathbf{2}}\mathbf{}\mathbf{+}\mathbf{}{\mathit{z}}^{\mathbf{2}\mathbf{}}+2xy-2xz-2yz=16 \\ U\sin gequation2. \\ \mathbf{30}+2xy-2xz-2yz=16 \\ 2xy-2xz-2yz=-14 \\ Finally,\mathit{x}\mathit{y}\mathit{}\mathit{}\mathit{-}\mathit{x}\mathit{z}\mathit{}\mathit{-}\mathit{}\mathit{y}\mathit{z}\mathit{}\mathit{=}\mathit{}\mathit{-}\mathit{7} \end{gathered}$$