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The expression {x+(x^3 -1)^0.5}^5 + {x -( x^3 -1)^0.5)^5 is a polynomial of degree? Please explain with formula.


The expression {x+(x^3 -1)^0.5}^5 + {x -( x^3 -1)^0.5)^5 is a polynomial of degree? Please explain with formula.


Grade:10

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
9 years ago

Hi Amin,

 

You need to binomially expand both the flower brackets in the question.

All odd powers will get cancelled, and the even powers will add up.

 

The highest power will come from the term

x*[(x^3-1)^0.5]^4 = x(x^3-1)^2. So the highest power will be 7.

Hence degree is 7.

 

Hope it helps.

 

Wish you all the best.

 

Regards,

Ashwin (IIT Madras).

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