Question

a^2+1/a^2=27then find a-1/a

Answer 1

${a}^{2} + \frac{1}{ {a}^{2} } = 27$

Now,

Let x = $a + \frac{1}{a}$

Then,

$a + \frac{1}{a} = x \\ ( {a + \frac{1}{a}) }^{2} = {x}^{2} \\ {a}^{2} + \frac{ {1}^{2} }{ {a}^{2} } +( 2 \times a \times \frac{1}{a} ) = {x}^{2} \\ {a}^{2} + \frac{1}{ {a}^{2} } + 2 = {x}^{2} \\ 27 + 2 = {x}^{2} \\ 29 = {x}^{2} \\ \sqrt{29} = x\\ x =\sqrt{29}$

Answer 2

Answer :-

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• Given :-

a² + 1 / a² = 27

• To find :-

a - 1 / a

• Salutation :-

a² + 1 / a² = 27

( a )² + ( 1 / a )² = 27

( a - 1 / a )² + 2 a × 1 / a = 27

[ • a² + b² = ( a + b )² - 2 ab → Using this identity ]

( a - 1 / a )² + 2 = 27 [ • a × 1 / a = 1 ]

( a - 1 / a )² = 27 - 2 = 25

( a - 1 / a )² = ( 5 )²

( a - 1 / a ) = 5 [ ★ Required answer ]

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Note :-

we know ,


Note :-

a² + b² = ( a + b )² - 2 ab ----- ( i )

a² + b² = ( a - b )² + 2ab ----- ( ii )


We can use both of the identity as needed here to find the answer we used the ( ii ) identity.

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