Given:
The equation is
[tex]2x^{\frac{5}{3}}-18x=0[/tex]
Required:
Find the non-zero solution to the equation.
Explanation:
The given equation is
[tex]2x^{\frac{5}{3}}-18x=0[/tex]
Rewrite the equation as:
[tex]2x^{\frac{5}{3}}=18x[/tex]
Divide both sides by 2.
[tex]x^{\frac{5}{3}}=9x[/tex]
Take cube on both sides.
[tex]\begin{gathered} (x^{\frac{5}{3}})^3=(9x)^3 \\ x^5=729x^3 \\ x^5-729x^3=0 \end{gathered}[/tex]
Take out common x
[tex]x^3[/tex][tex]x^3(x^2-729)=0[/tex]
Find the factor by using the formula
[tex]a^2-b^2=(a-b)(a+b)[/tex][tex]\begin{gathered} x^3(x-27)(x+27)=0 \\ x=0,27,-27 \end{gathered}[/tex]
Final Answer:
Thus the non-zero solutions to the given equation are x =27, -27.
