Question

Simplify √(x^2-10x+25) if -5≤x<5

Answer 1

$\qquad\qquad\huge\underline{{\sf Answer}}$

Let's simplify ~

$\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 10x + 25 }$

$\qquad \sf \dashrightarrow \: \sqrt{ {x}^{2} - 5x - 5x + 25 }$

$\qquad \sf \dashrightarrow \: \sqrt{ {x}^{} (x- 5) - 5(x - 5) }$

$\qquad \sf \dashrightarrow \: \sqrt{ (x- 5) (x - 5) }$

$\qquad \sf \dashrightarrow \: \sqrt{ (x- 5) {}^{2} }$

$\qquad \sf \dashrightarrow \: (x- 5)$

value x lies between :

$\qquad \sf \dashrightarrow \: - 5 \leqslant x \leqslant 5$

if the value of x is taken -5

$\qquad \sf \dashrightarrow \: - 5 - 5$

$\qquad \sf \dashrightarrow \: - 10$

if value of x is taken as 5

$\qquad \sf \dashrightarrow \:5 - 5$

$\qquad \sf \dashrightarrow \:0$

So, the possible values of the required expression lies between ~

$\qquad \sf \dashrightarrow \: - 10 \leqslant \sqrt{ {x}^{2} - 10x + 25 } < 0$

I hope you understood the whole procedure. let me know if you have any doubts in given steps ~