x²+y²=58

xy=21

x²+y²=58

x=21/y

(21/y)²+y²=58

441/y²+y²=58

441+y⁴=58y²

y⁴-58y²+441=0

t=y²

t²-58t+441=0

Δ=(-58)²-4*1*441

Δ=3364-1764

Δ=1600

√Δ=40

t₁=(-(-58)-40)/(2*1)
t₁=18/2

t₁=9

t₂=(-(-58)+40)/(2*1)
t₂=98/2

t₂=49

9=y²

y=-3 ∨ y=3

49=y²

y=-7 ∨ y=7

x=21/-3 ∨ x=21/3

x=-7 ∨ x=7

x=21/-7 ∨ x=21/7

x=-3 ∨ x=3

(-7,-3),(7,3),(-3,-7),(3,7)