Question

\( \begin{array}{l}\text { 26. } x^{3}\left(\frac{3}{x^{3}}-\sqrt{3}\right)=\frac{\sqrt{3}}{x^{3}}, \\ x^{54}+x^{36}+x^{18}+1=\text { ? } \\ \begin{array}{ll}\text { (a) }+2 & \text { (b) } 0 \\ \text { (c) }-2 & \text { (d) }+1\end{array}\end{array} \)

Answer 1

x³(3/x³-√3)=√3/x³   find x⁵⁴+x³⁶+x¹⁸+1

x³√3 (√3/x³-1)=√3/x³

 x³(√3/x³-1)=1/x³  

(√3- x³)=1/x³

√3=1/x³ + x³

(√3 )³ = ( 1/x³ + x³ )³

3√3  = 1/x9 + x9  + 3√3

1/x⁹ + x⁹  = 0

1 + x¹⁸   = 0

x¹⁸  = -1

Now x⁵⁴+x³⁶+x¹⁸+1  =  ( x¹⁸ )³ + ( x¹⁸ )² +  x¹⁸ + 1

=  ( -1 )³ + ( -1 )²  ( -1 ) +1  =  0