Question

U is the midpoint of TV. TU = x2 + 2x – 2. UV = -x + 8. Find the
positive value of x.

Answer 1

x = 2

Explanation:

It is given that,

U is the midpoint of TV.

TU = x² + 2x – 2

UV = -x+8

We need to find a positive value of x.

For midpoint,

TU = UV

Putting values,

x² + 2x – 2 = -x+8

or

x² + 2x – 2+ x - 8= 0

x² +3x-10 = 0

x² +5x - 2x -10 = 0

x(x+5) -2(x+5) = 0

(x-2) (x+5) = 0

x = +2 and x = -5

Hence, the positive value of x is 2.