( x 2y z ) #160; ^ 2 = x ^ 2 + 4y ^ 2 + z ^ 2 4xy+2yz 2xz ( a+b+c ) #160; ^ 2 = a ^ 2 + b ^ 2 + c ^ 2 +2ab+2bc+2ca ...

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Solving a Quadratic Equation by Completion of Squares Method

Evaluate x-...

Question

Evaluate ${(x - 2 y - z)}^{2}$

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Solution

${(x - 2 y - z)}^{2}$
$= x^{2} + {4 y}^{2} + z^{2} - 4 x y + 2 y z - 2 x z$
${(a + b + c)}^{2} = a^{2} + b^{2} + c^{2} + 2 a b + 2 b c + 2 c a$

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∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \frac{1}{z} & \frac{1}{z} & - \frac{(x + y)}{z^{2}} - \frac{(y + z)}{x^{2}} & \frac{1}{x} & \frac{1}{x} - \frac{y (y + z)}{x^{2} z} & \frac{x + 2 y + z}{x z} & - \frac{y (x + y)}{x z^{2}} \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣

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