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If x3 + y3 = 152 x + y = 8 Find the value of x4 + y4 + 14. |
706 701 720 715 |
720 |
x3 + y3 = 152 x + y = 8 (x + y)3 = x3 + y3 + 3xy (x + y) 512 = 152 + 24xy xy = \(\frac{360}{24}\) xy = 15 ⇒ x2 + y2 = 64 - 2 × 15 ⇒ x2 + y2 = 34 ⇒ x4 + y4 = (34)2 - 2 × 15 × 15 ⇒ x4 + y4 = 1156 - 450 = 706 x4 + y4 + 14 = 706 + 14 = 720 |
