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If a - 2b + 3c = 0; state the value of a3 - 8b3 + 27c3.
If x + 5y = 10; find the value of x3 + 125y3 + 150xy - 1000.
If a + b = 11 and a2 + b2 = 65; find a3 + b3.
If x, y and z are three different numbers, then prove that :
x2 + y2 + z2 - xy - yz - zx is always positive.