Question

anyone do HELp Me please ​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

$\red{\large\mathfrak {question}} \:$

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$\sf \: if \: {x}^{2} + \dfrac{1}{ {x}^{2} } = 7 \: \: \: find \: the \: values \: of \:$

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$\green{\large\mathfrak {answer}} \: \:$

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$\sf \: \red{ (i) \: \: \: x - \dfrac{1}{x} }$

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$\sf \: \blue{ ∵(x - { \dfrac{1}{x} )}^{2} = {x}^{2} - 2 \times x \times \dfrac {1}{x} + ( { \dfrac{1}{x}) }^{2} }$

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$\sf \: \blue{\implies (x - { \dfrac{1}{x} )}^{2} = {x}^{2} - 2 + \dfrac{1}{ {x}^{2} } }$

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$\sf \blue{\implies (x - { \dfrac{1}{x}) }^{2} = 7 - 2 \: \: \: \: \: \: \: \: \: \: \: ...( {x}^{2} + \dfrac{1}{ {x}^{2} } = 7)}$

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$\sf \blue{ \implies \: x - \dfrac{1}{x} = \sqrt{5} }$

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$\sf \: \red{ (ii) \: \: \: x + \dfrac{1}{x} }$

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$\sf \: \blue{ ∵(x + { \dfrac{1}{x} )}^{2} = {x}^{2} + 2 \times x \times \dfrac {1}{x} + ( { \dfrac{1}{x}) }^{2} }$

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$\sf \: \blue{\implies (x + { \dfrac{1}{x} )}^{2} = {x}^{2} + 2 + \dfrac{1}{ {x}^{2} } }$

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$\sf \blue{\implies (x + { \dfrac{1}{x}) }^{2} = 7 + 2 \: \: \: \: \: \: \: \: \: \: \: ...( {x}^{2} + \dfrac{1}{ {x}^{2} } = 7)}$

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$\sf \blue{ \implies \: x + \dfrac{1}{x} = \sqrt{9} }$

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$\sf \: \blue{ \implies \: \: \: x + \dfrac{1}{x} = 3}$

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$\sf \: \red{ (iii) \: \: \: 3{x}^{2} - \dfrac{3}{{x}^{2} }}$

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$\sf \: \blue{= \:\:\:3({x}^{2}- \dfrac{1}{{x}^{2}}) }$

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$\sf\blue{ ∵ {a}^{2}-{b}^{2}= (a+b)(a-b)}$

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$\sf \: \blue{\implies \:\:\:3({x}^{2}- \dfrac{1}{{x}^{2}}) = 3[(x+\dfrac{1}{x})(x-\dfrac{1}{x})]}$

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$\sf \: \blue{ \implies\:\:\:3({x}^{2}- \dfrac{1}{{x}^{2}}) = 3(3 × \sqrt{5}) \: \: \: \: \: \: \: \: \: \: ...( x + \dfrac{1}{x} = 3,x - \dfrac{1}{x} = \sqrt{5}) }$

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$\sf \: \blue{ \implies\:\:\:3({x}^{2}- \dfrac{1}{{x}^{2}}) = 9\times \sqrt{5} }$

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$\sf \: \blue{ \implies\:\:\:3{x}^{2}- \dfrac{3}{{x}^{2}}= 9 \sqrt{5} }$

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$\pink{\large\mathfrak {!! \:hope\: it \:helps \:you\: !!}} \:$