61. The value of $$\frac{{5.35 \times 5.35 \times 5.35 + 3.65 \times 3.65 \times 3.65}}{{53.5 \times 53.5 + 36.5 \times 36.5 - 53.5 \times 36.5}}{\text{is:}}$$
62. If 2x3 + ax2 + bx - 2 leaves the remainders 7 and 0 when divided by (2x - 3) and (x + 2), respectively, then the values of a and b are respectively:
63. If x2 - 3x - 1 = 0, then the value of (x2 + 8x - 1)(x3 + x-1)-1 is:
64. If a + b + c = 3 and none of a, b and c is equal to 1, then what is the value of $$\frac{1}{{\left( {1 - a} \right)\left( {1 - b} \right)}} + \frac{1}{{\left( {1 - b} \right)\left( {1 - c} \right)}} + \frac{1}{{\left( {1 - c} \right)\left( {1 - a} \right)}}?$$
65. A = $$\frac{{{x^8} - 1}}{{{x^4} + 1}}$$ and B = $$\frac{{{y^4} - 1}}{{{y^2} + 1}}.$$ If x = 2 and y = 9, then what is the value of A2 + 2AB + AB2?
66. If x2 - 12x + 33 = 0, then what is the value of (x - 4)2 + $$\frac{1}{{{{\left( {x - 4} \right)}^2}}}?$$
67. If a + b = 8 and a + a2b + b + ab2 = 128 then the positive value of a3 + b3 is:
68. If x2 + 16 = -4x, then what is the value of x3 - 64?
69. If x + y = 1, then what is the value of x3 + 3xy + y3?
70. If $$x - \frac{3}{x} = 6,\,x \ne 0,$$ then the value of $$\frac{{{x^4} - \frac{{27}}{{{x^2}}}}}{{{x^2} - 3x - 3}}$$
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