JAMB Mathematics Past Questions & Answers - Page 74

\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\)= m + n√6

\(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}\) x \(\frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - \sqrt{2}}\)


\(\frac{2 \sqrt{3} (\sqrt{3} - 2 \sqrt{2}) - \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}{\sqrt{3}(\sqrt{3} - 2 \sqrt{2}) + 2 \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}\)

\(\frac{2 \times 3 - 4\sqrt{6} - 6 + 2 \times 2}{3 - 2 \sqrt{6} + 2 \sqrt{6} - 4 \times 2}\)

= \(\frac{6 - 4 \sqrt{6} - \sqrt{6} + 4}{3 - 8}\)

= \(\frac{0 - 4 \sqrt{6} - 6}{5}\)

= \(\frac{10 - 5 \sqrt{6}}{5}\)

= − 2 + √6

∴ m + n\(\sqrt{6}\) = − 2 + √6

m = − 2, n = 1

(3√64a³)\(^{-1}\)

\(\frac{1}{(3√64a^3)

= \(\frac{1}{4a}\)

Gradient of line joining points (3, 2), (1, 4)

Gradient = \(\frac{\text{Change in Y}}{\text{Change in X}}\)

= \(\frac{y_2 - Y_1}{x_2 - x_1}\)\)

(X1, Y1) = (3, 2)

(X2, Y2) = (1, 4)

Gradient = \(\frac{4 − 2}{1 + 3}\)

= \(\frac{2}{-2}\)

= −1

x * y is an operation on 3x + 2y − 1

Find 3A − 1

x = 3, y = −1

3 * − 1 on 3x + 2y − 1

3(3) + 2(−1) −1

= 9 − 2 − 1

= 6

p = s + \(\frac{sm^2}{nr}\)

p = s + ( 1 + \(\frac{m^2}{nr}\))

p = s (1 + \(\frac{nr + m^2}{nr}\))

nr × p = s (nr + m2)

s = \(\frac{nrp}{nr + m^2}\)