Question

Alguem sabe (sistema irracional) x=7/3y x2+y2=232

Answer 1

vamos lá...

Sistema de equação pelo método da substituição

$x^2+y^2=232 \\ \\ \frac{x}{y} = \frac{7}{3} \\ \\ vamos~~isolar~~x \\ x= \frac{7y}{3} \\ \\ substituir~x~em \\ \\ x^2+y^2=232 \\ \\ ( \frac{7y}{3} )^2+y^2=232 \\ \\ \frac{49y^2}{9} +y^2=232 \\ \\ mmc=9 \\ \\ 49y^2+9y^2=2088 \\ 58y^2=2088 \\ y^2=2088\div58 \\ y^2=36 \\ \\ y=\pm \sqrt{36} \\ y=\pm6$ 

$se~~x= \frac{7y}{3} \\ para~y=+6 ~~~~~~~e ~~~~~~~~y=-6 \\ \\ x= \frac{7.6}{3} ~~~~~~~~~~~~~~~~~~~~~~~~x= \frac{7.(-6)}{3} \\ \\ x= \frac{42}{3} ~~~~~~~~~~~~~~~~~~~~~~~~~~x=- \frac{42}{3} \\ \\ x'=14~~~~~~~~~~~~~~~~~~~~~~~~~~~x"=-14 \\ \\ S=\{(14,6);(-14,-6)\}$