Question

Daca $4 x^{2} +9 y^{2} =256$ si 2x+3y=20 ; sa se calculeze xy, 2x-3y, x, y.

Answer 1

Ridici  ecuatia   2    la  patrat
(4x²+9y²)+12xy=400=>
1)(2x+3y)²=400=> 2x+3y=20  relatia 1
2) 256+12xy=400=>
12xy=144
xy=12=>
ridici2x-3y  la  patrat
4x²+9y²-12xy=256-144=112
(2x-3y)²=112
2x-3y=√112=4*√7  relatia 2
Din  relatia  1  si   2  faci  sistem
{2x+3y=20
{2x-3y=4√7=>  x=5+√7
y=(10-2√7)/3