Question

if px+qy=6 and qx-py=2 and x^2+y^2=4 find p^2+q^2

Answer 1

Hi ,

px + qy = 6

( px + qy )² = 36

p²x² + q² y² + 2pqxy = 36 ----( 1 )

similarly ,

q² x² + p² y² - 2pqxy = 4 ------( 2 )

add ( 1 ) and ( 2 ) we get ,

( p² + q² ) x² + ( p² + q² ) y² = 40

( p² + q² ) ( x² + y² ) = 40

( p² + q² ) × 4 = 40

[ x² + y² = 4 given ]

Therefore ,

p² + q² = 40/4

= 10

I hope this helps you.

:)