If X+y+z=2

Xy+xz+yz=-5

X^2 + y^2 + z^2 = 14

Find X, y, and z

Question

Mathematics

Enzo Chase

27 May, 16:36

If X+y+z=2

Xy+xz+yz=-5

X^2 + y^2 + z^2 = 14

Find X, y, and z

+1

Answers (1)

Know the Answer?

Judah Preston · Answer 1

If we substitute z = 2 - x - y in the last 2 equations it simplifies to 2 equations in x and y:=

x^2 + y^2 + xy - 2x - 2y = 5 and

-x^2 - y^2 - xy + 2x + 2y = - 5

if we add these we get 0 = 0 so there are infinite solutions

If X+y+z=2Xy+xz+yz=-5X^2 + y^2 + z^2 = 14Find X, y, and z

If X+y+z=2

Xy+xz+yz=-5

X^2 + y^2 + z^2 = 14

Find X, y, and z