Question

Qual a solução do sistema?
{X²+Y=11
{X+Y²=7

Answer 1

Resposta:

Vamos lá!

$\left \{ {{x^{2} +y=11} \atop {x+y^{2} =7}} \right. ||y=11-x^{2} \\\\x+(11-x^{2} )^{2}=7 \\\\x+121-22x^{2} +x^{4} =7\\\\x^{4} -22x^{2} +x+114=0$

Aplicando a Regra de Ruffini a partir de sua régua perpendicular, temos:

$x=3\\\\y=11-3^{2} \\\\y=2\\\\conferindo...\\x^{2} +y=11\\\\x^{2} =11-2\\\\x=\sqrt{9} \\\\x=3$