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 \: √( (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 ~