Question

Suppose a, b are positive real numbers such that a pa + b p b = 183, ap b + b pa = 182. Find 9 5 (a + b).

Answer 1

Acc to the question, apa + bpb = 183, apb + bpa = 182

or, p(a²+b²) = 183 ⇒ (a²+b²) = 183/p

or, p(2ab) = 182 ⇒ (2ab) = 182/p

or, (a²+b²) + (2ab) = 183/p + 182/p

or, (a + b)² = 365/p

or, (a + b) = $\sqrt{365/p}$ [Ans]

Therefore, 95 (a + b) = 95 $\sqrt{365/p}$