Решите систему уравнений [tex]\left \{ {{x^{2}+y^{2}=25} \atop {x+y=7}} \right.[/tex]. Created by Bаnan. algebra-ru

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July 2022 1 9 Report

Решите систему уравнений

[tex]\left \{ {{x^{2}+y^{2}=25} \atop {x+y=7}} \right.[/tex]

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julyap $x^{2} +y ^{2} =25 \\ x+y=7 \\ \\ y=7-x \\ \\ x^{2} +(7-x) ^{2} =25 \\ x^{2} +49+x^{2} -14x-25=0 \\ 2 x^{2} -14x+24=0|:2 \\ x^{2} -7x+12=0 \\ D=49-4*12=49-48=1 \\ \sqrt{D} =1 \\$

$x_{1} = \frac{7+1}{2} = \frac{8}{2} =4 \\ x_{2} = \frac{7-1}{2} = \frac{6}{2} =3 \\ \\ y_{1} =7-4=3 \\ y _{2} =7-3=4 \\ \\ \\ \left \{ {{y=3} \atop {x=4}} \right. \ \ \left \{ {{4=2} \atop {x=3}} \right.$

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