Question 125

If $$\sqrt{4x-9}+\sqrt{4x+9}=5+\sqrt{7}$$, then the value of $$x$$ is

Solution

given that

$$\sqrt{4x-9}+\sqrt{4x+9}=5+\sqrt{7}$$

$$\sqrt{4x-9} - 5 = \sqrt{7} - \sqrt{4x+9}$$

on squaring both sides

4x - 9 + 25 + 10$$\sqrt{4x+9}$$ = 7 + 4x + 9 - 2$$\sqrt{28x+63}$$

10$$\sqrt{4x-9}$$ = 2$$\sqrt{28x+63}$$

on squaring both sides again

400x - 900 = 112x + 252

288x = 1152

x = 4

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