If a³ + b³ = 6240 and a + b = 30, then find the value of {(a + b)² – 3ab}

If [x + (1/x)] = 3, find [x² + (1/x²)].

Evaluate (998)³ without multiplying directly.

If a + b + c = 5, a³ + b³ + c³ = 85 and abc =25, then find the value of a² + b² + c² – ab –bc – ca

If, 6x + y = 20, and 2xy = 32, and 6x > y, then find the value of 216x³ – y³.

If (a² + 1/a²) = 18, then find the value of (a³ - 1/a³).

Length of each side of a rhombus is 13 cm and one of the diagonal is 24 cm. What is the area (in cm²) of the rhombus?

If a + b + c = 14 and ab + bc + ca = 60, then find the value of a² + b² + c².