Question

Aflati numerele consecutive x si y stiind ca:a)x ori y=240,b)x ori y=420,c)x ori y=600

Answer 1

$\displaystyle x,y \ nr \ consecutive\implies y=x+1 \\ \\ a)x(x+1)=240 \\ \\ x^2+x-240=0 \\ \\ \Delta=1-4*1*(-240)=961 \\ \\ x_1=\dfrac{-1+\sqrt{961}}{2*1}=15 \\ \\ x_2=\dfrac{-1-\sqrt{961}}{2*1}=-16 \\ \\ x=15 \ sau \ -16 \ ; \ y=16 \ sau \ -15 \\ \\ b)x(x+1)=420 \\ \\ x^2+x-420=0 \\ \\ \Delta=1-4*1*(-420)=1681 \\ \\ x_1=\dfrac{-1+\sqrt{1681}}{2*1}=20 \\ \\ x_2=\dfrac{-1-\sqrt{1681}}{2*1}=-21 \\ \\ x=20 \ sau \ -21 \ ; \ y=21 \ sau \ -20 \\ \\ c)x(x+1)=600 \\ \\ x^2+x-600=0 \\ \\ \Delta=1-4*1*(-600)=2401 \\ \\ x_1=\dfrac{-1+\sqrt{2401}}{2*1}=24 \\ \\ x_2=\dfrac{-1-\sqrt{2401}}{2*1}=-25 \\ \\ x=24 \ sau \ -25 \ ; \ y=25 \ sau \ -24$