Question

Please help! i cant figure it out

Answer 1

y = 3, y = - 1

Explanation:

P is the centroid of the triangle.

Centroid of a triangle divides the median in the ratio 2 : 1

Therefore,

BP : PV = 2 : 1

`(BP)/( PV) = (2)/(1) \\ \\ \frac{ {y}^(2) + 1 }{y + 2} = (2)/(1) \\ \\ {y}^(2) + 1 = 2y + 4 \\ \\ {y}^(2) + 1 - 2y - 4 = 0 \\ \\ {y}^(2) - 2y - 3 = 0 \\ \\ {y}^(2) - 3y + y - 3 = 0 \\ \\ y(y - 3) + 1(y - 3) = 0 \\ \\ (y - 3)(y + 1) = 0 \\ \\ y - 3 = 0 \: \: or \: \: y + 1 = 0 \\ \\ y = 3, \: \: y = - 1`