Question

(a+1/a)²-(a -1/a)² expand using algebraic formula answer is 2 a²+1/a² but I need explanation
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Answer 1

Hey!!

Answer:

As, (a+b)²=a²+2ab+b²

(a–b)²=a²–2ab+b²

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

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

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

=$\frac{a {}^{4} + 2a {}^{2} + 1}{a {}^{2} } - ( \frac{a {}^{4} - 2a {}^{2} + 1 }{a {}^{2} } )$

=$\frac{ {a}^{4} + 2a {}^{2} + 1 - {a}^{4} +2a {}^{2} - 1 }{a {}^{2} }$

=$\frac{4a {}^{2} }{a {}^{2} }$

$= 4$

Answer is '4'!

Answer 2

Step-by-step explanation:

(a+b)²=a²+2ab+b²

(a–b)²=a²–2ab+b²

( a + \frac{1}{a} )^{2} - (a - \frac{1}{a} )^{2}(a+

a

1

)

2

−(a−

a

1

)

2

=

=( \frac{a ^{2} + 1}{a} ) {}^{2} - ( \frac{a {}^{2} - 1}{a} ) {}^{2}(

a

a

2

+1

)

2

−(

a

a

2

−1

)

2

=( \frac{(a {}^{2} + 1) {}^{2} }{a {}^{2} } ) - ( \frac{ ({a}^{2} + 1) {}^{2} }{a {}^{2} } )(

a

2

(a

2

+1)

2

)−(

a

2

(a

2

+1)

2

)

=\frac{a {}^{4} + 2a {}^{2} + 1}{a {}^{2} } - ( \frac{a {}^{4} - 2a {}^{2} + 1 }{a {}^{2} } )

a

2

a

4

+2a

2

+1

−(

a

2

a

4

−2a

2

+1

)

=\frac{ {a}^{4} + 2a {}^{2} + 1 - {a}^{4} +2a {}^{2} - 1 }{a {}^{2} }

a

2

a

4

+2a

2

+1−a

4

+2a

2

−1

=\frac{4a {}^{2} }{a {}^{2} }

a

2

4a

2

= 4=4