Answer:
There are two pairs of numbers:
-8 -18
and
18 8
Explanation:
a * b = 144 EQ. 1
a - b = 10 EQ. 2
From EQ. 2:
a = 10 + b EQ. 3
Replacing EQ. 3 in EQ. 1:
(10+b)b = 144
10*b + b*b = 144
b² + 10b - 144 = 0
b = {-10±√((10²)-(4*1*-144))} / (2*1)
b = {-10±√(100+576)} / 2
b = {-10±√676} / 2
b = {-10±26} / 2
b₁ = {-10-26} / 2 = -36/2 = -18
b₂ = {-10+26} / 2 = 16/2 = 8
a₁ - b₁ = 10
a₁ - (-18) = 10
a₁ + 18 = 10
a₁ = 10 - 18
a₁ = -8
a₂ - b₂ = 10
a₂ - 8 = 10
a₂ = 10 + 8
a₂ = 18
Check:
a₁ * b₁ = -8 * -18 = 144
a₂ * b₂ = 8 * 18 = 144