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Explanation:

Given, $\sqrt{5x+9}$ + $\sqrt{5x-9}$ = 6 + 3√2

⇒ $\sqrt{5x+9}$ + $\sqrt{5x-9}$ = √36 + √18

∴ $\sqrt{5x+9}$= √36 and $\sqrt{5x-9}$= √18

⇒ 5x + 9 = 36 and 5x - 9 = 18

⇒ 5x = 27

⇒ 10x = 54

⇒ 10x + 9 = 63

⇒ $\sqrt{10x+9}$ = √63

⇒ $\sqrt{10x+9}$ = 3√7

Hence, option (a).