Question

please do urgent ..please guys​

Answer 1

Answer:

34

Step-by-step explanation:

1,771 = 7 × 11 × 23;

1,771 is not a prime, is a composite number;

66 = 2 × 3 × 11;

66 is not a prime, is a composite number;

Answer 2

Option - D ✔ (23)

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Step-by-step Explanation :

Given :-

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$\displaystyle \sf⟼ \: \: log \: \bigg(\frac{x + y}{5} \bigg) \: = \: \frac{1}{2} \: \bigg(log \: x \: + \: log \: y \bigg)$

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To Find :-

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$\displaystyle \sf⟼ \: \: What \: is \: the \: value \: of \: \: \frac{x}{y} \: + \: \frac{y}{x}$

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Explanation :

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Given that,

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$\displaystyle \sf⟼ \: \: log \: \bigg(\frac{x + y}{5} \bigg) \: = \: \frac{1}{2} \: \bigg(log \: x \: + \: log \: y \bigg)$

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$\displaystyle \sf⟼ \: \: log \: \bigg(\frac{x + y}{5} \bigg) \: = \: \frac{1}{2} \: \bigg(log \:x \: + \: y \bigg)$

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$\displaystyle \sf⟼ \: \: \frac{x + y}{5} \: = \: log \:_{x} \frac{1}{2} \: + \: log \:_{y} \frac{1}{2}$

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$\displaystyle \sf⟼ \: \: \frac{x + y}{5} \: = \: log \:_{xy} \frac{1}{2}$

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$\displaystyle \sf⟼ \: \: \frac{x + y}{5} \: = \: log \: \sqrt{xy}$

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$\displaystyle \sf⟼ \: \: \frac{x + y}{5} \: = \: \frac{ \sqrt{xy} }{1}$

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By Cross Multiplication,

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$\displaystyle \sf⟼ \: \: x + y \: = \: 5 \: \sqrt{xy}$

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Squaring on both sides,

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$\displaystyle \sf⟼ \: \: (x + y )^{2} \: = \: (5 \: \sqrt{xy} )^{2}$

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$\displaystyle \sf⟼ \: \: {x}^{2} \: + \: y ^{2} \: + \: 2xy \: = \: 5 \: \sqrt{xy} \: \times \: 5 \: \sqrt{xy}$

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$\displaystyle \sf⟼ \: \: {x}^{2} \: + \: y ^{2} \: + \: 2xy \: = \: 25 xy$

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$\displaystyle \sf⟼ \: \: {x}^{2} \: + \: y ^{2} \: = \: 25 xy \: - \: 2xy$

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$\displaystyle \sf⟼ \: \: {x}^{2} \: + \: y ^{2} \: = \: 23xy$

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$\displaystyle \sf⟼ \: \: \frac{{x}^{2} \: + \: y ^{2}}{xy} \: = \: 23$

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$\displaystyle \sf⟼ \: \: \cancel \frac{ {x}^{2} }{xy} \: + \: \cancel\frac{ {y}^{2} }{xy} = \: 23$

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$\displaystyle \bf⟼ \: \: \frac{ {x} }{y} \: + \: \frac{ {y}}{x} = \: 23$

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Hence,

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$\displaystyle \sf⟼ \: \: The \: \: value \: \: of \: \: \frac{x}{y} \: + \: \frac{y}{x} \: \: \: is \: \: \bf 23$

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