Question

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:

• A. 2
• B. 3
• C. 1
• D. 0

Answer 1

Answer: (C)

1

Answer 2

(x−1)(x−3)​+(x−3)(x+3)​
=4(x−412​)(x−42​)​
⇒x−3​=0⇒x=3 which is in domain
or
x−1​+x+3​=4x−2​
2(x−1)(x+3)​=2x−4
x2+2x−3=x2−4x+4
6x=7
x=7/6(rejected)