Question

$left { {{ sqrt{xy}=6} atop {x^2+y^2=97}} right.$

Answer 1

xy >= 0
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V(xy) = 6 => xy = 36
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x^2 + y^2 + 2xy - 2xy = 97
(x+y)^2 - 2xy = 97
(x+y)^2 - 2*36 = 97
(x+y)^2 = 169
x+y = 13
y = 13-x
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x*(13-x) = 36
x^2 - 13x + 36 = 0
x1 = 4
x2 = 9
y1 = 9
y2 = 4