Given that a(a + 2b) = 104/3 and b^2 = 7/9 then find |a + b|.
b^2 =7/9
b =sqrt(7/9)
a(a + 2*sqrt(7/9) =104/3, solve for a
a^2 + 2*sqrt(7/9)a =104/3
Solve for a:
a^2 + (2 sqrt(7) a)/3 = 104/3
Add 7/9 to both sides:
a^2 + (2 sqrt(7) a)/3 + 7/9 = 319/9
Write the left hand side as a square:
(a + sqrt(7)/3)^2 = 319/9
Take the square root of both sides:
a + sqrt(7)/3 = sqrt(319)/3 or a + sqrt(7)/3 = -sqrt(319)/3
Subtract sqrt(7)/3 from both sides:
a = sqrt(319)/3 - sqrt(7)/3 or a + sqrt(7)/3 = -sqrt(319)/3
Subtract sqrt(7)/3 from both sides:
a = sqrt(319)/3 - sqrt(7)/3 or a = -sqrt(7)/3 - sqrt(319)/3
Abs[a + b] =sqrt(319) / 3