Question

expansion of (x + 1/x)² is​

Answer 1

Answer:

x*2 +2x1/x +1/x*2

x*2+2x+1/x*2

Answer 2

To find -

Expand - ( x + 1/x )² .

Solution -

Here , assuming that x = a and (1/x) = b .

Now , we know that -

( a + b )² = a² + 2ab + b² .

=> ( x + 1/x )² = x² + 2 + 1/x² .

Similarly we can say that -

=> ( x - 1/x )² = x² + 1/x² - 2 .

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Additional Information -

( a + b )² = a² + 2ab + b²

( a - b )² = a² - 2ab + b²

( a + b )( a - b ) = a² - b²

( a + b )³ = a³ + 3ab ( a + b ) + b³

( a - b )³ = a³ - 3ab ( a + b ) - b³

( a + b + c )³ = a³ + b³ + c³ + 3 ( a + b )( b + c )( c + a )

a³ + b³ + c³ - 3abc = ( a + b + c )( a² + b² + c² - ab - bc - ca )

When a + b + c = 0 ,

a³ + b³ + c³ = 3abc .

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