Question

a soma das idade de duas irmãs é igual a 8 e a soma dos quadrados das suas idades é 34 qual e a idade delas

Answer 1

$\large\boxed{\begin{array}{l}\begin{cases}\rm x+y=8\\\rm x^2+y^2=34\end{cases}\\\begin{cases}\rm y=8-x\\\rm x^2+y^2=34\end{cases}\\\\\rm x^2+(8-x)^2=34\\\rm x^2+64-16x+x^2=34\\\rm 2x^2-16x=34-64\\\rm 2x^2-16x=-30\\\rm 2x^2-16x+30=0\div2\\\rm x^2-8x+15=0\end{array}}$

$\large\boxed{\begin{array}{l}\rm\Delta=b^2-4ac\\\rm\Delta=(-8)^2-4\cdot1\cdot15\\\rm\Delta=64-60\\\rm\Delta=4\\\rm x=\dfrac{-b\pm\sqrt{\Delta}}{2a}\\\\\rm x=\dfrac{-(-8)\pm\sqrt{4}}{2\cdot1}\\\\\rm x=\dfrac{8\pm2}{2}\begin{cases}\rm x_1=\dfrac{8+2}{2}=\dfrac{10}{2}=5\\\\\rm x_2=\dfrac{8-2}{2}=\dfrac{6}{2}=3\end{cases}\end{array}}$

$\large\boxed{\begin{array}{l}\rm para\,x=5\\\rm y=8-x\\\rm y=8-5\\\rm y=3\\\rm para\,x=3\\\rm y=8-x\\\rm y=8-3\\\rm y=5\\\rm S=\{(5,3),(3,5)\}\end{array}}$

$\large\boxed{\begin{array}{l}\rm Uma\,irm\tilde a\,possui\,5\,anos\,e\,a\,outra\,3\,anos\end{array}}$