2019 · Q11
Let a and b be two positive real numbers such that a√a + b√b = 32 and a√b + b√a = 31. What is the value of 5(a + b)/7?
Elementary MathematicsAlgebra
- A5
- B7
- C9
- DCannot be determined
Explanation
Put x = sqrt(a), y = sqrt(b). Then x^3+y^3 = 32 and xy(x+y) = 31. With s = x+y, p = xy: s^3-3ps = 32 and ps = 31, so s^3 = 125, s = 5, p = 31/5. Then a+b = x^2+y^2 = s^2-2p = 25-62/5 = 63/5. Hence 5(a+b)/7 = 63/7 = 9.