81. If 2x + 3y - 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx ?
82. If x + y = 4, xy = 2, y + z = 5, yz = 3, z + x = 6 and zx = 4, then find the value of x3 + y3 + z3 - 3xyz.
83. If x = 2 - p, then x3 + 6xp + p3 is equal to:
84. Simplify the following expression:
$$\frac{{{{\left( {{a^2} - 4{b^2}} \right)}^3} + 64{{\left( {{b^2} - 4{c^2}} \right)}^3} + {{\left( {16{c^2} - {a^2}} \right)}^3}}}{{{{\left( {a - 2b} \right)}^3} + {{\left( {2b - 4c} \right)}^3} + {{\left( {4c - a} \right)}^3}}}$$
$$\frac{{{{\left( {{a^2} - 4{b^2}} \right)}^3} + 64{{\left( {{b^2} - 4{c^2}} \right)}^3} + {{\left( {16{c^2} - {a^2}} \right)}^3}}}{{{{\left( {a - 2b} \right)}^3} + {{\left( {2b - 4c} \right)}^3} + {{\left( {4c - a} \right)}^3}}}$$
85. x is a negative number such that k + k-1 = -2, then what is the value of $$\frac{{{k^2} + 4k - 2}}{{{k^2} + k - 5}}?$$
86. If a + b + c = 2, $$\frac{1}{a} + \frac{1}{b} + \frac{1}{c}$$ = 0, ac = $$\frac{4}{b}$$ and a3 + b3 + c3 = 28, find the value of a2 + b2 + c2.
87. If x = $$2 - {2^{\frac{1}{3}}} + {2^{\frac{2}{3}}},$$ then find the value of x3 - 6x2 + 18x.
88. If a + b + c + d = 2, then the maximum value of (1 + a)(1 + b)(1 + c)(1 + d) is:
89. If 3a = 4b = 6c and a + b + c = $$27\sqrt {29} $$ then $$\sqrt {{a^2} + {b^2} + {c^2}} $$ is equal to
90. If $$\frac{{{x^2} + 1}}{x} = 4\frac{1}{4},$$ then what is the value of $${x^3} + \frac{1}{{{x^3}}}?$$
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