For any three positive real numbers a, b and c, $9 ({25 a}^{2} + b^{2}) + 25 (c^{2} - 3 a c) = 15 b (3 a + c) .$ . Then

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Solution

$\begin{matrix} 9 (25 a^{2} + b^{2}) + 25 (c^{2} - 3 a c) = 15 b (3 a + c) 2254 a^{2} + 9 b^{2} + 25 c^{2} - 75 a c - 45 a b - 15 b c = 0 \frac{1}{2} [{(15 a - 3 b)}^{2} + {(3 b - 5 c)}^{2} + {(5 c - 15 a)}^{2}] = 0 15 a = 3 b = 5 c \end{matrix}$

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Similar questions

9 (25 a^{2} + b^{2}) + 25 (c^{2} - 3 a c) = 15 b (3 a + c)

a, b

c

9 (25 a^{2} + b^{2}) + 25 (c^{2} - 3 a c) = 15 b (3 a + c)

a, b

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9 (25 a^{2} + b^{2}) + 25 (c^{2} - 3 a c) = 15 b (3 a + c) .

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