please help!

Given that g + 7f = 12f - 5g evaluate $\sqrt{\frac{17g^2}{2f^2+8g^2}}$

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$g + 7f = 12f - 5g\\ f=\frac{6g}{5}\\ f^2=\frac{36g^2}{25}$

$\sqrt{\frac{17g^2}{2f^2+8g^2}}=\sqrt{\frac{17g^2}{2(\frac{36g^2}{25})+8g^2}}=\sqrt{\frac{17g^2\cdot25}{2\cdot 36g^2+200g^2}} =\sqrt{\frac{425g^2}{272g^2}}\color{blue}=1.25$

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