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CAT 2023 Set-1 | Quantitative Aptitude | Question: 2

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Square on both sides $(\sqrt{5x+9} + \sqrt{5x-9})^{2} = 9(2+\sqrt2)^2$ . After opening the square and adding/subtracting some terms we will get $5x + \sqrt{(5x)^2 - 9^2} = 27 + 18\sqrt{2}$.

Compare $ 5x$ with $27$ and $\sqrt{(5x)^2-9^2}$ with $18\sqrt2$ we will get $x=5.4$

putting the value into the equation $\sqrt{10*5.4 +9}$ we are getting $\sqrt{63}$ which is equal to $3\sqrt7$

Hence option $A$ is the answer.
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