Question

The real numbers x and y satisfy the nonlinear system of equations

Answer 1

\[ \huge 2x^2-6xy+2y^2+43x+43y=174\]
\[\huge x^2+y^2+5x+5y=30\]

Answer 2

wat i did
\[2(x^2+y^2)-6xy+43(x+y)=174\]
\[2(x+y)^2-2xy+5(x+y)=30\]

Answer 3

Find the largest possible value of \[\left| xy \right|\]

Answer 4

One branch of hyperbola intersects circle 4 points
2x^2 - 6xy + 2y^2 + 43x + 43y =174, 2x^2 + 2y^2 + 10x +10y = 60
33x + 33y - 6xy = 114
xy = [11(x + y) - 38]/2

4 intersections with |xy| values
(1, 3), --> 3
(3, 1), --> 3
(-2, 4), --> 8
(4, -2) --> 8
largest possible value is 8

Answer 5

u get it i help u aut work the problem

Answer 6

its very clear thanks to you @johana