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| 1. |
Find 2^{3} + 8y^{3} if xy =2 and x+2y =5 |
| Answer» 27X 3 +8Y 3 =(3X) 3 +(2Y) 3 =(3x+2y)[(3x) 2 −(3x×2y)+(2y) 2 ](∵a³+b³=(a+b)(a²−ab+b²))=12[(3x) 2 −(6×xy)+(2y) 2 ](∵3x+2y=12,xy=6)=12[(3x) 2 −(6×6)+(2y) 2 ]=12[(3x) 2 −36+(2y) 2 ]=12[(3x) 2 +(2y) 2 +(2×3x×2y)−(2×3x×2y)−36]=12[(3x+2y) 2 −12xy−36]=12[(12) 2 −(12×6)−36]=12(144−72−36)=12(144−108)=12×36=432Hence, 27x 3 +8y 3 =432. | |