Question

已知a+b=10,a^2=23,b^2=3 求 a^3-b^3

Answer 1

【1】20=23-3=a²-b²=(a+b)(a-b)=10(a-b).∴a-b=2.【2】100=10²=(a+b)²=a²+2ab+b²=23+3+2ab,∴2ab=100-(23+3)=74,∴ab=37.【3】a³-b³=(a-b)(a²+ab+b²)=2(23+37+3)=126.∴a³-b³=126