a distancia entre os pontos A (x,1) e (-2,4) é 5. determine a abscissa do ponto A
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Olá, Deivid.
![\sqrt{[x-(-2)]^2+(1-4)^2}=5\Rightarrow\\\\
(x+2)^2+9=5^2\Rightarrow\\\\
x^2+4x+4+9-25=0\Rightarrow\\\\
x^2+4x-12=0\Rightarrow\\\\
\Delta=16+48=64\Rightarrow \sqrt\Delta=\pm8\Rightarrow\\\\
x=\frac{-4\pm8}{2}\Rightarrow\\\\\boxed{x_1=2}\text{ ou }\boxed{x_2=-6}](https://tex.z-dn.net/?f=%5Csqrt%7B%5Bx-%28-2%29%5D%5E2%2B%281-4%29%5E2%7D%3D5%5CRightarrow%5C%5C%5C%5C%0A%28x%2B2%29%5E2%2B9%3D5%5E2%5CRightarrow%5C%5C%5C%5C%0Ax%5E2%2B4x%2B4%2B9-25%3D0%5CRightarrow%5C%5C%5C%5C%0Ax%5E2%2B4x-12%3D0%5CRightarrow%5C%5C%5C%5C%0A%5CDelta%3D16%2B48%3D64%5CRightarrow+%5Csqrt%5CDelta%3D%5Cpm8%5CRightarrow%5C%5C%5C%5C%0Ax%3D%5Cfrac%7B-4%5Cpm8%7D%7B2%7D%5CRightarrow%5C%5C%5C%5C%5Cboxed%7Bx_1%3D2%7D%5Ctext%7B+ou+%7D%5Cboxed%7Bx_2%3D-6%7D "\sqrt{[x-(-2)]^2+(1-4)^2}=5\Rightarrow\\\\
(x+2)^2+9=5^2\Rightarrow\\\\
x^2+4x+4+9-25=0\Rightarrow\\\\
x^2+4x-12=0\Rightarrow\\\\
\Delta=16+48=64\Rightarrow \sqrt\Delta=\pm8\Rightarrow\\\\
x=\frac{-4\pm8}{2}\Rightarrow\\\\\boxed{x_1=2}\text{ ou }\boxed{x_2=-6}")
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