1) primer numero: ``x´´ segundo numero: ``y´´
[tex] \left \{ {{x+y=40} \atop {x*y=76}} \right. [/tex] ===>
[tex] \left \{ {{x=40-y} \atop {(40-y)*y=76}} \right. [/tex] ===>
[tex]40y-y^2=76[/tex] ===> [tex]y^2-40y+76 = 0[/tex] ===>
[tex]y = \frac{40+- \sqrt{1600-304} }{2}= \frac{40+-36}{2} [/tex] ===>
[tex] \left \{ {{y=38} \atop {y=2}} \right. [/tex]
[tex] \left \{ {{x=40-38=2} \atop {x=40-2=38}} \right. [/tex]
Solución:
x = 38 , y = 2
x= 2 , y 38 Tiene dos soluciones
2) Largo: ``x´´ Altura: ``y´´
[tex] \left \{ {{2x+2y=36} \atop {x*y=80}} \right. [/tex] ===>
[tex] \left \{ {{x =18-y} \atop {(18-y)*y=80}} \right. [/tex] ===>
[tex]18y-y^2=80 [/tex] ===> [tex]y^2-18y+80 = 0[/tex] ===>
[tex]y=\frac{18+-\sqrt{324-320}}{2}=\frac{18+-2}{2}[/tex] ===>
[tex] \left \{ {{y=10 cm} \atop {y=8 cm}} \right. [/tex] ===>
[tex] \left \{ {{x=18-10=8cm} \atop {x=18-8 = 10cm}} \right. [/tex]
Solución:
x = 8 cm , y = 10 cm
x = 10 cm , y = 8 cm Tiene dos soluciones
espero que te sirva y que lo entiendas
saludos!!
