Respostas

2013-08-08T18:04:25-03:00
São os números 6 e 7.  6x6= 36, 7x7= 49, 36+49= 85.
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2013-08-08T18:08:51-03:00
x^2+(x+1)^2=85\\\\
x^2+x^2+2x+1=85\\\\
2x^2+2x-84=0\Longrightarrow x^2+x-42=0\\\\
\Delta=b^2-4\cdot a\cdot c\\
\Delta=1^-4\cdot1\cdot(-42)\\
\Delta=1+168\\
\Delta=169\\\\
x=\dfrac{-b\pm\sqrt{\Delta}}{2a}=\dfrac{-1\pm\sqrt{169}}{2\cdot1}=\dfrac{-1\pm13}{2}\\\\
\Longrightarrow x_1=\dfrac{-1+13}{2}=\dfrac{12}{2}=6\\\\
\Longrightarrow x_2=\dfrac{-1-13}{2}=\dfrac{-14}{2}=-7

Então, ou os números são 6 e 7:

x=6\hspace{2.0cm}x+1=7

Ou são -7 e -6:

x=-7\hspace{2.0cm} x+1=-6


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