The number of real roots of the equation (x^2+1 )^3 x^3 + x^2+1 3 x =0,(x 0) is

Step-by-step solution

Given equation, (x^2+1 )^3 x^3 + x^2+1 3 x =0(x 0) 3 (x^2+1 )^3+x^2 (x^2+1 ) 3 x^3 =0 (x^2+1 ) [3 (x^2+1 )^2+x^2 ]=0 ...(i) aligned & x^2 0 & (x^2+1 ) 1 and 3 (x^2+1 )^2+x^2 3 aligned By using this result in Eq. (i), we can observe that for no real value of x will satisfy Eq. (i). Hence, the number of real roots is zero.