Ques. If x^5-x^3+x=2 then x^6 belongs to

Soln. x(x^4-x^2+1)=2,

multiplying by x^2+1 we get
x(x^6+1)=2(x^2+1)
=>x^6+1=2(x+1/x)>=4

so x^6 belongs to 3<=x

I cant understand how they factorized it and why multiplied with x^2+1 only

Thank u

hi Swap Bho,

since we need the interval of x^6 , therefore somehow we need to bring a " x^6" term in the given expression in the easiest possible way. Multiplying with x^2+1 to x^4-x^2+1 brings the expression x^6+1 using the identity a^3+b^3. hence solved in this way.  

Thank you