In parallelogram ABCD , diagonals AC¯¯¯¯¯ and BD¯¯¯¯¯ intersect at point E, BE=2x2−x , and DE=x2+6 .What is BD ?

AC and BC intercept each other at point E. So E is a point on BD.

Then BE + DE = BD. That gives us

[tex]BD = 2x^2-x+x^2+6=3x^2-x+6[/tex]

The answer is [tex]BD=3x^2-x+6[/tex]