Question

Resolva o sistema de equação do 2° grau: {x-y=10 x2+y2=82

Answer 1

Explicação passo-a-passo:

pra facilitar, pus os cálculos em anexo. qualquer dúvida, pergunte nos comentários.

Answer 2

$\begin{cases}\mathsf{x-y=10}\\\mathsf{x^2+y^2=82}\end{cases}$

$\begin{cases}\mathsf{x=y+10}\\\mathsf{x^2+y^2=82}\end{cases}$

$\mathsf{(y+10)^2+y^2=82}\\\mathsf{y^2+20y+100+y^2-82=0}\\\mathsf{2y^2+20y+18=0\div2}\\\mathsf{y^2+10y+9=0}\\\mathsf{a=1~~b=10~~~c=9}\\\mathsf{\Delta=b^2-4ac}\\\mathsf{\Delta=10^2-4\cdot1\cdot9}\\\mathsf{\Delta=100-36}\\\mathsf{\Delta=64}\\\mathsf{y=\dfrac{-b\pm\sqrt{\Delta}}{2a}}\\\mathsf{y=\dfrac{-10\pm\sqrt{64}}{2\cdot1}}\\\mathsf{y=\dfrac{-10\pm8}{2}}\begin{cases}\mathsf{y_1=\dfrac{-10+8}{2}=-\dfrac{2}{2}=-1}\\\mathsf{y_2=\dfrac{-10-8}{2}=-\dfrac{18}{2}=-9}\end{cases}\\\mathsf{se~y=-1\implies~x=-1+10=9}\\\mathsf{se~y=-9\implies x=-9+10=1}</p><p>\\\large\boxed{\boxed{\boxed{\boxed{\mathsf{S=\{(1,-9),(9,-1)\} }}}}}$

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