Question

The number of solutions of the equation $\sqrt{4-x}=x-2$ is

• A. 1
• B. 1.0
• C. 01

Answer 1

Answer: (A), (B), (C)

Given: $\sqrt{4-x}=x-2$
Squaring both sides, we get:
$4-x=(x-2{)}^2\Rightarrow 4-x=x^2-4x+4\Rightarrow x^2-3x=0\Rightarrow x(x-3)=0\Rightarrow x=0\&x=3$

But substituting both the values of $x$ in the original equation, we get for $x=0,$
$\sqrt{4-0}=0-2\Rightarrow \sqrt{4}=-2$ which is not possible.
Thus, $x=0$ is an extraneous root of the quadratic equation.
Similarly, on substituting $x=3$ in the equation above, we get:
$\sqrt{4-3}=3-2$ which is true.
Hence, $3$ is the solution for the given equation.
Thus, number of solutions is $1$