71) If \(x^4 + y^4 + x^2y^2 = 21\) and \(x^2 + y^2 - xy = 7\), then what is the value of \[ \frac{x}{y} + \frac{y}{x}? \]

• (a) \(\frac{3}{4}\)
• (b) \(-\frac{3}{2}\)
• (c) \(\frac{5}{2}\)
• (d) \(\frac{5}{4}\)

72) If \(x + y = 3\), and \[ \frac{1}{x} + \frac{1}{y} = \frac{3}{10}, \] then what is the value of \(x^2 + y^2\)?

• (a) 28
• (b) 34
• (c) 29
• (d) 26

73) Simplify: \[ \frac{(375 + 125)^2 - (125 - 375)^2}{375 \times 375 - 125 \times 125} \]

• (a) \(\frac{15}{8}\)
• (b) \(\frac{3}{4}\)
• (c) \(\frac{3}{2}\)
• (d) \(\frac{27}{28}\)

74) If \(x^2 - 5\sqrt{2}x + 1 = 0\), then the value of \[ \frac{x^3 + \frac{1}{x}}{x^2 + 1} \] is:

• (a) \(\frac{12\sqrt{2}}{5}\)
• (b) \(\frac{24\sqrt{2}}{5}\)
• (c) \(\frac{26\sqrt{2}}{5}\)
• (d) \(\frac{18\sqrt{2}}{5}\)

75) What is the constant term in the expansion of \[ \left(5x^2 - \frac{1}{x}\right)^3? \]

• (a) 5
• (b) -15
• (c) 15
• (d) 75

76) If \(x + y + z = 1\), \(xy + yz + zx = xyz = -4\), then what is the value of \[ x^3 + y^3 + z^3? \]

• (a) -1
• (b) -8
• (c) 1
• (d) 8

77) If \(a^3 - b^3 = 2349\) and \(a - b = 9\), then \[ (a + b)^2 - ab \] is equal to:

• (a) 261
• (b) 280
• (c) 229
• (d) 244

78) If \(x - \frac{1}{x} = \sqrt{77}\), then one of the values of \[ x^3 + \frac{1}{x^3} \] is:

• (a) -702
• (b) \(77\sqrt{77}\)
• (c) \(3\sqrt{77}\)
• (d) \(80\sqrt{77}\)

79) If \(a + b + c = 0\), then the value of \[ \frac{(b + c)^2}{bc} + \frac{(c + a)^2}{ca} + \frac{(a + b)^2}{ab} \] is:

• (a) 1
• (b) -3
• (c) -1
• (d) 3

80) If \(a^2 + b^2 + c^2 + 216 = 12(a + b - 2c)\), then \[ \sqrt{ab} - bc - ca \] is:

• (a) \(6\sqrt{5}\)
• (b) \(4\sqrt{5}\)
• (c) \(3\sqrt{5}\)
• (d) \(8\sqrt{5}\)

81) If \[ 2a + \frac{3}{a} - 1 = 11, \] what is the value of \[ 4a^2 + \frac{9}{a^2}? \]

• (a) 110
• (b) 148
• (c) 132
• (d) 121

82) If \[ \frac{x}{y} + \frac{y}{x} = 2,\ (x \ne y), \] then the value of \((x - y)\) is:

• (a) -2
• (b) 1
• (c) 2
• (d) 0

83) If \[ \frac{56\sqrt{7}x^3 - 2\sqrt{2}y^3}{2(\sqrt{7}x - \sqrt{2}y)} = Ax^2 + By^2 - Cxy, \] then the value of \[ A + B - \sqrt{14}C \] is:

• (a) 19
• (b) 10
• (c) 58
• (d) 38

84) If \[ \sqrt{x} - \frac{1}{\sqrt{x}} = \sqrt{7}, \] then the value of \[ x^2 + \frac{1}{x^2} \] is:

• (a) 60
• (b) 75
• (c) 81
• (d) 79

85) If \(x + y + z = 3\), \(xy + yz + zx = -12\) and \(xyz = -16\), then the value of \[ \sqrt[3]{x^3 + y^3 + z^3 + 13} \] is:

• (a) 11
• (b) 9
• (c) 10
• (d) 8