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Evaluation of a Determinant

27. If 2x+3y=...

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27. If 2x+3y=5, prove that 22x+33y-55+330xy=0

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\frac{1}{2 (2 x + 3 y)} + \frac{12}{7 (3 x - 2 y)} = \frac{1}{2}, \frac{7}{(2 x + 3 y)} + \frac{4}{(3 x - 2 y)} = 2

, then the value of

(2 x + 3 y)

\frac{1}{2 (2 x + 3 y)} + \frac{12}{7 (3 x - 2 y)} = \frac{1}{2}

\frac{7}{2 x + 3 y} + \frac{4}{3 x - 2 y} = 2

2 x + 3 y \neq 0

3 x - 2 y \neq 0

.

2^{x} = 3^{y} = 6^{z}

(\frac{1}{x} + \frac{1}{y} - \frac{1}{z} = 0)

2^{x} = 3^{y} = 12^{z}

- \frac{2}{x} + \frac{1}{y} + \frac{1}{z} = 0

(2 x - 3 y) (2 x + 3 y) = (2 x)^{2} - (3 y)^{2}

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