Question

how to solve p^2q^2+3pqx+2x^2by completing the square method

Answer 1

Hi ,

2x² + 3pqx + p² q² = 0

divide each term with 2 , we get

x² + 3/2 pqx + p² q²/2 = 0

x²+2× x ×(3pq/4)+(3pq/4)² = (- p²q²/2 )+(3pq/4)²

( x + 3pq/4 )² = (- p² q² )/4 + ( 9p²q² ) / 16

= ( - 4p²q² + 9p²q² ) / 16

= ( 5p²q² ) / 16

Therefore ,

x + 3pq / 4 = ± √[ 5p²q² / 16 ]

= ± ( pq / 4 )√5

x = [ ( -3pq ± √5 pq )] / 4

x = ( pq / 4 ) [ -3 ± √5 ]

I hope this helps you.

:)