Quadratic Equation Question 8
Question 8 - 31 January - Shift 1
The number of real roots of the equation $\sqrt{x^{2}-4 x+3}+\sqrt{x^{2}-9}=\sqrt{4 x^{2}-14 x+6}$, is:
(1) 0
(2) 1
(3) 3
(4) 2
Show Answer
Answer: (2)
Solution:
Formula: Roots of equations
$\sqrt{(x-1)(x-3)}+\sqrt{(x-3)(x+3)}$
$=\sqrt{4(x-\frac{12}{4})(x-\frac{2}{4})}$
$\Rightarrow \sqrt{x-3}=0 \Rightarrow x=3$ which is in domain
or
$\sqrt{x-1}+\sqrt{x+3}=\sqrt{4 x-2}$
$2 \sqrt{(x-1)(x+3)}=2 x-4$
$x^{2}+2 x-3=x^{2}-4 x+4$
$6 x=7$
$x=7 / 6$
The number of real root is 1.
