РЕШИТЕ СИСТЕМУ УРАВНЕНИЙ x^2+y^2=26 xy=5

Question

РЕШИТЕ СИСТЕМУ УРАВНЕНИЙ x^2+y^2=26 xy=5

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http://tex.z-dn.net/?f=x%5E2+%2B+y%5E2+%3D+26%5C%5C+xy+%3D+-5%5C%5C+x%5E2+%2B+y%5E2+%2B2xy-2xy%3D+26%5C%5C+xy+%3D+-5%5C%5C+%28x%2By%29%5E2%3D26%2B2xy%5C%5C+%28x%2By%29%5E2%3D26%2B2%2A%28-5%29%5C%5C+%28x%2By%29%5E2%3D16%5C%5C+x%2By%3D4%5C%5Cxy%3D-5%5C%5Cx%3D4-y%5C%5C4y-y%5E2%2B5%3D0%5C%5Cy%5E2-4y-5%3D0%5C%5Cy_1%3D-1%5C%5Cy_2%3D5%5C%5Cx_1%3D5%5C%5Cx_2%3D-1%5C%5Cx%2By%3D-4%5C%5Cxy%3D-5%5C%5Cx%3D-4-y%5C%5C-4y-y%5E2%2B5%3D0%5C%5Cy%5E2%2B4y-5%3D0%5C%5Cy_3%3D1%5C%5Cy_4%3D-5%5C%5Cx_3%3D-5%5C%5Cx_4%3D1%5

Answer 1

X=5/y
25/y² + y²=26
y^4-26y²+25=0
y²=a
a²-26a+25=0
a1+a2=26 U a1*a2=25
a1=1⇒y²=1
y1=-1⇒x1=-5
y2=1⇒x2=5
a2=25⇒y²=25
y3=-5⇒x3=-1
y4=5⇒x4=1