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
