Question
If 9x² + y² = 37 and xy=2, x, y>0, then the
value of (27x³ + y³) is:Solution
27x3 + y3 = (3x + y) (9x2 + y2 – 3xy) = use (a + b)2 = a2 + b2 + 2ab = (3x + y)2 = ax2 + y2 + 6xy = (3x + y)2 = 37 + 6 × 2 = 49 = 3x + y = 7 = 27x3 + y3 = 7 × (37 – 3 × 2) = 27x3 + y3 = 7 × 31 = 217
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