Question

решить систему уравнений: $left { {{x-5y=2} atop {x^2-y=10}} right.$

Answer 1

x-5y=2
x²-y=10

x=2+5y
(2+5y)²-y=10

x=2+5y
4+20y+25y²-y-10=0

x=2+5y
25y²+19y-6=0

25y²+19y-6=0
D=19²-4*(-6)*25=361+600=961=31²
$y_{1}= frac{-19- sqrt{961} }{2*25} = frac{-19-31 }{50} = frac{-50}{50} =-1 \ y_{2}= frac{-19+sqrt{961} }{2*25} = frac{-19+31 }{50} = frac{12}{50} =0.24$

x=2+5y
y₁ = -1
y₂=0.24

x₁=2-5
x₂=2+1,2
y₁ = -1
y₂=0.24

x₁= -3
x₂=3,2
y₁ = -1
y₂=0.24