Question : If $x$ = $y$ = $z$, then $\frac{\left (x+y+z \right )^{2}}{x^{2}+y^{2}+z^{2}}$ is equal to:
Option 1: 4
Option 2: 2
Option 3: 3
Option 4: 1
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Correct Answer: 3
Solution :
According to the question, $x$ = $y$ = $z$
We can put $x$ at the place of $y$ and $z$.
Given equation:
$\frac{\left (x+y+z \right )^{2}}{x^{2}+y^{2}+z^{2}}$ = $\frac{(x+x+x)^2}{x^2+x^2+x^2}$
⇒ $\frac{\left (x+y+z \right )^{2}}{x^{2}+y^{2}+z^{2}}$ = $\frac{(3x)^2}{3x^2}$
⇒ $\frac{\left (x+y+z \right )^{2}}{x^{2}+y^{2}+z^{2}}$ = $\frac{9x^2}{3x^2}$
⇒ $\frac{\left (x+y+z \right )^{2}}{x^{2}+y^{2}+z^{2}}$ = 3
Hence, the correct answer is 3.
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