Question

In parallelogram ABCD , diagonals AC and BD intersect at point E, BE=2x^2−x , and DE=x^2+6 .

What is BD ?

Answer 1

BD=BE+ED=2x²-x+x²+6=3x²-x+6

Answer 2

BE = DE

2x^2-x = x^2+6

x^2-x-6 =0

(x+2) (x-3)

x = -2 or x = 3

1 solution using x = -2:

BE = 2(-2)^2 -(-2) = 10

DE = (-2)^2+6 = 10

10 +10 =20

2nd solution using x = 3

BE =2(3)^2-3 = 15

DE = (3)^2+6 =15

15+15 = 30

The answer could be 20 or 30. Will need to try them both

Would probably try 30 first ( maybe x can't be a negative number?)