WAEC - Mathematics (2013 - No. 11)
If x = 64 and y = 27, evaluate: \(\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}\)
2\(\frac{1}{5}\)
1
\(\frac{5}{11}\)
\(\frac{11}{43}\)
설명
\(\frac{x^{\frac{1}{2}} - y^{\frac{1}{3}}}{y - x^{\frac{2}{3}}}\)
substitute x = 64 and y = 27
\(\frac{64^{\frac{1}{2}} - 27^{\frac{1}{3}}}{27 - 64^{\frac{2}{3}}} = \frac{\sqrt{64} - 3\sqrt{27}}{27 - (3\sqrt{64})^2}\)
= \(\frac{8 - 3}{27 - 16}\)
= \(\frac{5}{11}\)
substitute x = 64 and y = 27
\(\frac{64^{\frac{1}{2}} - 27^{\frac{1}{3}}}{27 - 64^{\frac{2}{3}}} = \frac{\sqrt{64} - 3\sqrt{27}}{27 - (3\sqrt{64})^2}\)
= \(\frac{8 - 3}{27 - 16}\)
= \(\frac{5}{11}\)