Question

The product of the real roots of the equation, $x^2+18x+30=2\sqrt{x^2+18x+45}$, is

• A. $20$
• B. $24$
• C. $16$
• D. $18$

Answer 1

The correct option is A $20$

$x^2+18x+30=2\sqrt{x^2+18x+45}$

Adding $16$ on both sides. We get,

$x^2+18x+45-2\sqrt{x^2+18x+45}+1=16$

$\Rightarrow {(\sqrt{x^2+18x+45}-1)}^2=16$

$\Rightarrow \sqrt{x^2+18x+45}-1=\pm 4$

$\Rightarrow \sqrt{x^2+18x+45}=\pm 4+1$

$\Rightarrow \sqrt{x^2+18x+45}=5$ or $\sqrt{x^2+18x+45}=-3$

$\Rightarrow x^2+18x+45=25,$ (Reject $-3$)

$\Rightarrow x^2+18x+20=0$

Product of root $=\frac{c}{a}=20$.