1.

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»

<P>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}


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