Question

if a^2+1/a^2=23,find the value of(a+1/a)

Answer 1

${a}^{2} + \frac{1}{ {a}^{2} } = 23 \\ \\ \\ \\ add \: \: \: \: \: 2(a \times \frac{1}{a} ) \: \: \: on \: both \: sides$

${a}^{2} + \frac{1}{ {a}^{2} } + 2(a \times \frac{1}{a} ) = 23 + 2( a\times \frac{1}{a} )$


By formula, (a + b)² = a² + b² + 2ab


Here,



${(a + \frac{1}{a} )}^{2} = 23 + 2 \\ \\ \\ {(a + \frac{1}{a} )}^{2} = 25 \\ \\ \\ a + \frac{1}{a} = \sqrt{25} \\ \\ a + \frac{1}{a} = 5$


I hope this will help you


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Answer 2

here is your answer
${a}^{2} + \frac{1}{ {a}^{2} } = 23 \\ \\ ( {a + \frac{1}{a} )}^{2} = {a}^{2} + ( { \frac{1}{a}) }^{2} + 2 \times a \times \frac{1}{a} \\ \\ ( {a + \frac{1}{a} )}^{2} = 23 + 2 \\ \\ ( {a + \frac{1}{a}) }^{2} = 25 \\ \\ a + \frac{1}{a} = \sqrt{25} \\ \\ = a + \frac{1}{a} = 5$
this is your answer
hope his helps you
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