First slide

Theory of equations

Question

If $\sqrt{3 x^{2} - 7 x - 30} + \sqrt{2 x^{2} - 7 x - 5} = x + 5,$ then $x$ is equal to

Moderate

A

2
B

3
C

6
D

5

Solution

$\sqrt{3 x^{2} - 7 x - 30} + \sqrt{2 x^{2} - 7 x - 5} = x + 5$
$\sqrt{3 x^{2} - 7 x - 30} = (x + 5) - \sqrt{2 x^{2} - 7 x - 5}$
on squaring $\sqrt{2 x^{2} - 7 x - 5} = 5$
$2 x^{2} - 7 x - 30 = 0 \Rightarrow x = 6$

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