Question

x+y = 8
x.y = 12

Calcule o valor de x² + y²
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Answer 1

Resposta:

2+6=8

2.6=12

X=2×2=4

Y=6×6=36

X=2

Y=6

x2=4

y2=36

36+4=40

X2+Y2=40

Answer 2

Resposta:

O resultado da expressão é  $\mathbf{x^2+y^2=40}$

Explicação passo-a-passo:

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$x+y=8\\\\y=8-x\\\\\\\\x\;.\;y=12\\\\x\;.\;(8-x)=12\\\\8x-x^2=12\\\\-x^2+8x-12=0$

Usando Bhaskara,

$a=-1\\b=8\\c=-12\\\\\\\Delta=b^2-4\;.\;a\;.\;c\\\Delta=8^2-4\;.\;-1\;.\;-12\\\Delta=64-48\\\Delta=16\\\\\\x=\dfrac{-b\pm\sqrt{\Delta}}{2\;.\;a}\\\\\\x=\dfrac{-8\pm\sqrt{16}}{2\;.\;-1}\\\\\\x=\dfrac{-8\pm4}{-2}\\\\\\x_1=\dfrac{-8+4}{-2}=\dfrac{-4}{-2}=2\\\\\\x_2=\dfrac{-8-4}{-2}=\dfrac{-12}{-2}=6$

Portanto, podemos ter

$x=2\;e\;y=6\\ou\\x=6\;e\;y=2$

Em ambos os casos teremos

$x^2+y^2=2^2+6^2=4+36=40\\ou\\x^2+y^2=6^2+2^2=36+4=40$