Question

6) If x² + y² = 7xy then show that
2 log (x+y)= log x + log y + 2 log 3​

Answer 1

Answer:

Sorry I can't understand your question.

Answer 2

Given :-

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$\bf⟼ \: \: {x}^{2} + {y}^{2} \: = \: 7xy$

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To Prove :-

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$\bf⟼ \: \: 2 \: log \: (x + y) \: = \: log \: x \: + \: log \: y \: + \: 2 \: log \: 3$

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Solution :-

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Given that,

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$\bf⟼ \: \: {x}^{2} + {y}^{2} \: = \: 7xy$

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Adding 2xy on both sides,

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$\bf⟼ \: \: {x}^{2} + {y}^{2} + 2xy\: = \: 7 xy + 2xy$

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$\bf⟼ \: \: ({x} + {y})^{2} \: = \: 9xy \: \: \: \: \: \: \: \: \: \bigg( ∴( {a + b)}^{2} \: = \: {a}^{2} + {b}^{2} + 2ab \bigg)$

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Adding log on both sides,

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$\bf⟼ \: \: log \: ({x} + {y})^{2} \: = \: log \: 9xy$

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$\bf⟼ \: \: 2 \: log \: ({x} + {y}) \: = \: log \: 9 \: + \: log \: x \: + \: log \: y$

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$\bf⟼ \: \: 2 \: log \: ({x} + {y}) \: = \: log \: {3}^{2} \: + \: log \: x \: + \: log \: y$

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$\bf⟼ \: \: 2 \: log \: ({x} + {y}) \: = \: 2 \: log \: {3} \: + \: log \: x \: + \: log \: y \:$

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Hence,

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$\bf \purple{⟼}\red{ \: \: 2 \: log \: ({x} + {y}) \: = \: log \: x \: + \: log \: y \: + \: 2 \: log \: {3}}$

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Hence, proved !!!

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