Question

Numerele intregi X si Y,pentru care 5x=2y si x ori y=10.Cu tot cu rezolvare va roggg.

Answer 1

Bună! ⭐

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x, y ∈ Z

$\left \{ {{5x=2y} \atop {x*y=10}} \right. => \left \{ {{5x-2y=0} \atop {x=\frac{10}{y} }} \right. =>$

$=> 5*\frac{10}{y} -2y=0 /*y=>$

$=> 50-2y^{2} =0 =>$

$=> -2y^{2} =-50=> y^{2} =25 => {\boxed{\mathbf{y_{1} =2; y_{2} =-2}}$

$Pentru$ $y_{1} => x_{1} = \frac{10}{2} =5 => {\boxed{\mathbf{x_{1} =5}}$

$Pentru$ $y_{2} => x_{2}=\frac{10}{-2} =-5 => {\boxed{\mathbf{x_{2} =-5}}$

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$(x_{1} , y_{1} )=(2, 5)$

$(x_{2} , y_{2} )=(-2,-5)$