TS EAMCET · Maths · Sequences and Series
If \(x\) and \(y\) are two positive integers such that \(x+2 y=10\) and \(x^2 y^3\) is maximum then \(x^2+2 y^3=\)
- A 34
- B 137
- C 43
- D 70
Answer & Solution
Correct Answer
(D) 70
Step-by-step Solution
Detailed explanation
\(x = 10 - 2y\) \(P = x^2 y^3 = (10 - 2y)^2 y^3\) \(\frac{dP}{dy} = 10y^2(10-2y)(3-y) = 0\) \(y = 3\) (since \(x, y > 0\)) \(x = 10 - 2(3) = 4\) \(x^2 + 2y^3 = 4^2 + 2(3^3) = 16 + 2(27) = 16 + 54 = 70\)
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