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the expression [x+(xpower3-1)power1/2 ]power5+[x-(xpower3-1)power1/2]power5. is a polynomial of degree plz solve immediately with full steps thank you.

the expression


[x+(xpower3-1)power1/2 ]power5+[x-(xpower3-1)power1/2]power5. is a polynomial of degree


 


plz solve immediately with full steps thank you.

Grade:12

2 Answers

SAGAR SINGH - IIT DELHI
878 Points
13 years ago

Dear student,

Use binomial theorem....

\begin{displaymath} (a+b)^n = a^n + n a^{n-1}b + {n(n-1)\over 2} a^{n-2}b^2 + ... + b^n \end{displaymath}


But what are all those terms in the middle? We write them in terms of combination notation

 

\begin{displaymath} \left(\!\!\! \begin{array}{c} n \\ m \end{array} \!\!\!\right) = \frac{n!}{m!(n-m)!} \end{displaymath}

This means the "combination of n things taken m at a time". This is also sometimes written as $ {^n}C_m$. Then we can write the binomial expansion as
\begin{displaymath} (a+b)^n = \sum_{m=0}^n \left(\!\!\! \begin{array}{c} n \\ m \end{array} \!\!\!\right) a^m b^{n-m} \end{displaymath}

ravi kumar tyagi
16 Points
13 years ago

hello bhaiya ji ,

                  can you solve all steps and also polynomial of this eqn

 

thank you for reply

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