Question

The product of the roots of the equation$\sqrt{x^2-4x+3}+\sqrt{x^2-7x+12}=3\sqrt{x-3}$ is

• A. 15
• B. -15
• C. 20
• D. -20

Answer 1

Answer: (A)

$\sqrt{x^2-4x+3}+\sqrt{x^2-7x+12}=3\sqrt{x-3}$
is defined for $x=3$ or $x\ge 4$.
Write (1) as
$\sqrt{x-3}[\sqrt{x-1}+\sqrt{x-4}]=3\sqrt{x-3}$
$\Rightarrow x=3\text{ or }\sqrt{x-1}+\sqrt{x-4}=3$
$\Rightarrow x=3\text{ or }\sqrt{x-1}=3-\sqrt{x-4}$
$\Rightarrow x=3\text{ or }x-1=9-6\sqrt{x-4}+x-4$
$\Rightarrow x=3\text{ or }6\sqrt{x-4}=6$
$\Rightarrow x=3\text{ or }x=5$
$\text{ Thus, product of roots }=15$.