(7 * x^2 - 16) / (3 * x^(2 / 3)) when x = 4/ 7\sqrt{7}

asked by guest
on Nov 26, 2024 at 6:19 am



You asked:

Calculate the value of 7x2−163x23\frac{7 {x}^{2} - 16}{3 {x}^{\frac{2}{3}}} when x=47x = \frac{4}{\sqrt{7}}.

MathBot Answer:

7x2−163x23=0\frac{7 {x}^{2} - 16}{3 {x}^{\frac{2}{3}}} = 0

7x2−163x23=(7(47)2−16)3(47)23=(7(477)2−16)3(477)23=7⋅167−163(477)23=(7⋅167−16)2833⋅4=0\begin{aligned}\frac{7 x^{2} - 16}{3 x^{\frac{2}{3}}}&=\frac{\left(7 \left(\frac{4}{\sqrt{7}}\right)^{2} - 16\right)}{3 \left(\frac{4}{\sqrt{7}}\right)^{\frac{2}{3}}}\\&=\frac{\left(7 \left(\frac{4 \sqrt{7}}{7}\right)^{2} - 16\right)}{3 \left(\frac{4 \sqrt{7}}{7}\right)^{\frac{2}{3}}}\\&=\frac{\frac{7 \cdot 16}{7} - 16}{3 \left(\frac{4 \sqrt{7}}{7}\right)^{\frac{2}{3}}}\\&=\frac{\left(\frac{7 \cdot 16}{7} - 16\right) \sqrt[3]{28}}{3 \cdot 4}\\&=0\end{aligned}


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