Question 38

If $$\sqrt{5x-6}+\sqrt{5x+6}=6$$, then what is the value of x ?

Solution

Given : $$\sqrt{5x-6}+\sqrt{5x+6}=6$$

Squaring both sides,

=> $$(\sqrt{5x-6})^2+(\sqrt{5x+6})^2+2(\sqrt{5x-6})(\sqrt{5x+6})=(6)^2$$

=> $$(5x-6)+(5x+6)+2\sqrt{25x^2-36}=36$$

=> $$10x+2\sqrt{25x^2-36}=36$$

=> $$\sqrt{25x^2-36}=18-5x$$

Again squaring both sides, we get :

=> $$25x^2-36 = 324 + 25x^2-180x$$

=> $$180x=324+36 = 360$$

=> $$x=\frac{360}{180}=2$$

=> Ans - (C)

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