Data:
age of Dollah = x (unknown element)
age of Fatimeh = x + 5 (age of Dollah + 5)
the product is 234
Equation:
x * (x + 5) = 234
x² + 5x = 234
x² + 5x - 234 = 0
Δ = b² - 4 a c = 5² - 4 (1 * -234) = 25 - 4 (-234) = 25 - (-936)
= 25 + 936 = 961
x₁,₂=[tex]\frac{b^{2} ± \sqrt{delta} }{2a}[/tex] = [tex]\frac{5^2 +/- \sqrt{961} }{2}[/tex] = [tex]\frac{25 +/- 31}{2}[/tex]
x1 = (25+31)/2 = 56 / 2 = 28
x2 = (25 -31)/2 = -6 / 2 = -3 [age can't be negative, so the first one is accettable]
So:
Dollah's age (x) = 28 years old
Fatima's age (x + 5) = 28 + 5 = 32 years old
