Question

Simplify √(x^2-10x+25) if -5≤x<5

Answer 1

`\\ \rm\Rrightarrow √(x²-10x+25)`

`\\ \rm\Rrightarrow √(x²-5x-5x+25)`

`\\ \rm\Rrightarrow √(x(x-5)-5(x-5))`

`\\ \rm\Rrightarrow √((x-5)(x-5))`

`\\ \rm\Rrightarrow √((x-5)^2)`

`\\ \rm\Rrightarrow\pm (x-5)`

Solution set(for x-5)

• {-10,-9,-8,-7,-4,-3,-2,-1,0}

for 5-x

• {0,-1,-2,-3,-4,-5,-6,-7,-8,-9,-10}

Answer 2

First, simplify the expression under the square root sign by factoring:

`\implies x^2-10x+25`

`\implies x^2-5x-5x+25`

`\implies x(x-5)-5(x-5)`

`\implies (x-5)(x-5)`

`\implies (x-5)^2`

Therefore:

`\implies √(x^2-10x+25)=√((x-5)^2)`

`\implies √(x^2-10x+25)=\pm(x-5)`

`\implies √(x^2-10x+25)=|x-5|`

As the domain is -5 ≤ x < 5, then:

`\implies y=-x+5`

and the range is 0 < y ≤ 10