Question

10. Aflati numerele naturale consecutive x si y, stiind ca:
a) x y = 240; b)x.y = 420;
c) x y = 600;
d)x-y=756.

Dau coroana!

Answer 1

Răspuns:

Explicație pas cu pas:

a) 15*16 = 240

b) 20*21 = 420

c) 24*25 = 600

d) 27*28 = 756

Answer 2

a)

$\it Fie\ \ x\ \ \c{s}i\ \ x+1\ \ cele\ \ dou\breve a\ \ numere\ \ consecutive\\ \\ x\cdot(x+1)=240\ \Rightarrow \ x^2+x=240 \Rightarrow x^2+x-240=0\\ \\ \Delta\ =1+4\cdot240=961\\ \\ \\ x_{1,2}=\dfrac{-1\pm\sqrt{961}}{2}=\dfrac{-1\pm29}{2}\ \stackrel{x>0}{\Longrightarrow}\ x=\dfrac{-1+29}{2} \Rightarrow x=14$

Numerele cerute  sunt  14  și  15.