Question

Решите систему уравнений
$left { {{x²+y²=58} atop {xy=21}} right.$

Answer 1

$left { {{ x^{2} + y^{2} =58} atop {y= frac{21}{x} }} right. }$
$x^{2} + (frac{21}{x}) ^{2} =58$
$x^{2} + frac{441}{ x^{2} } =58$
$x^{4} - 58 x^{2} + 441 = 0$
$t = x^{2}$
$t^{2} - 58 t + 441 = 0$
$D = 3364 - 4*441=1600$
$t_{1} = frac{58+40}{2}=49$
$t_{2} = frac{58-40}{2}=9$
$x_{1}=sqrt{49} = 7$
$x_{2}=sqrt{49} = -7$
$x_{3}=sqrt{9} = 3$
$x_{4}=sqrt{9} = -3$
$y_{1}=frac{21}{7}= 3$
$y_{2}=frac{21}{-7}= -3<span>$
$y_{3}=frac{21}{3}= 7<span>$
$y_{4}=frac{21}{-3}= -7<span>$