Question

If 2,5 and x,6 are the endpoints of a segment with length √17,what is the value of x ?

Answer 1

`x=6` or `x=-2`

Explanation:

By the Pythagorean Theorem
`color(white)("XXX")sqrt((x-2)^2+(6-5)^2)=sqrt(17)`

`color(white)("XXX")(x-2)^2+1=17`

`color(white)("XXX")x^2-4x+4+1-17=0`

`color(white)("XXX")x^2-4x-12=0`

`color(white)("XXX")(x-6)(x+2)=0`

So `x=6` or `x=-2`