Se considera doua numere naturale a si b care indeplinesc conditiile: b-a =15 si a×b=250 Atunci suma nr. a+b are valoarea
a)20
b)25
c)30
d)35
e)40

b-a = 15 => b = 15 + a

axb = 250

a x(15+a) = 250 => 15a + a² = 250 => a²+15a - 250 =0 => a= [(-15+√(225+1000)]/2

a₁= (-15+35)/2 = 10 ∈ N ; a₂ = -25 ∉ N

b = 15+10 = 25

10x25 = 250 => a=10 ; b=25 solutii corecte. ∈ N   a+b = 10+25 = 35

Varianta 2

(b-a)² = 15² = 225 = b²-2ab+a²

(a+b)² = b²+2ab+a²

(a+b)²-(b-a)² = b²+2ab+a²-b²+2ab-a² = 4ab = 4 x 250 = 1000

(a+b)² = 4ab + (b-a)² = 1000 + 225 = 1225

a+b = √(1225) = 35

b-a=15

b=25

a=10

b=25-10=15

a*b=250

25*10=250

a+b=25+10=35

Bafta!