61. If x + y + z = 10, x3 + y3 + z3 = 75 and xyz = 15, then find the value of x2 + y2 + z2 - xy - yz - zx.
62. If x + y + z = 17, xyz = 171 and xy + yz + zx = 111, then the value of $$\root 3 \of {\left( {{x^3} + {y^3} + {z^3} + xyz} \right)} $$ is:
63. If x + y = 14 and x3 + y3 = 1064, then the value of (x - y)2 is:
64. If $$p + \frac{1}{p} = 112,$$ find the value of $${\left( {p - 112} \right)^{15}} + \frac{1}{{{p^{15}}}} = ?$$
65. If x = 1 + √2 + √3, then find the value of x2 - 2x + 4.
66. If a2 + b2 + c2 + 96 = 8(a + b - 2c), then $$\sqrt {ab - bc - ca} $$ is equal to
67. If $$x + \frac{1}{x} = \frac{{\sqrt 3 + 1}}{2},$$ then what is the value of $${x^4} + \frac{1}{{{x^4}}}?$$
68. If x = 2 + √3, then find the value of x4 - 8x3 + 16x2.
69. The value of $$\frac{{7 + 8 \times 8 \div 8\,{\text{of }}8 + 8 \div 8 \times 4\,{\text{of }}4}}{{4 \div 4\,{\text{of }}4 + 4 \times 4 \div 4 - 4 \div 4\,{\text{of}}\,{\text{2}}}}{\text{is:}}$$
70. If $$3\sqrt {\frac{{1 - a}}{a}} + 9 = 19 - 3\sqrt {\frac{a}{{1 - a}}} ,$$ then what is the value of a?
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