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

1 Answer

Jun 26, 2018

$x = 6$ $x=6$ or $x = - 2$ $x=-2$

Explanation:

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

$XXX {(x - 2)}^{2} + 1 = 17$ $color(white)("XXX")(x-2)^2+1=17$

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

$XXX x^{2} - 4 x - 12 = 0$ $color(white)("XXX")x^2-4x-12=0$

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

So $x = 6$ $x=6$ or $x = - 2$ $x=-2$

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