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  4. Number of real values of x satisfying the equation √x2-6 x+9+√x2-6 x+6=1 text is

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Q. Number of real values of $x$ satisfying the equation
$\sqrt{x^2-6 x+9}+\sqrt{x^2-6 x+6}=1 \text { is }$

Complex Numbers and Quadratic Equations

Solution:

$\left(x^2-6 x+9\right)-\left(x^2-6 x+6\right)=3 $
$\sqrt{x^2-6 x+9}-\sqrt{x^2-6 x+6}=3$
$\text { adding } \sqrt{x^2-6 x+9}=2$
$x^2-6 x+9=4$
$x^2-6 x+5=0$
$(x-5)(x-1)=0 \Rightarrow x=1 \text { or } 5$but none satisfies.