F.3數學題(20點)

1. 10×16⁸+17×16⁷=10×16⁸+(16+1)16⁷=10×16⁸+16⁸+16⁷=11×16⁸+16⁷=B00000000₁₆+10000000₁₆=B10000000₁₆ [C]2. 5²ºº⁹+15(5²ºº⁸)-5²º¹º=5²ºº⁹+3(5²ºº⁹)-5(5²ºº⁹)=5²ºº⁹(1+3-5)=5²ºº⁹(-1)=-5²ºº⁹ [D]3. (√3+2)²ºº⁹×(2-√3)²º¹º=(2+√3)²ºº⁹(2-√3)²ºº⁹(2-√3)=[(2+√3)(2-√3)]²ºº⁹(2-√3)=(2²-√3²)²ºº⁹(2-√3)=1²ºº⁹(2-√3)=2-√3 [C]4._________________3x+1/x=10 ________________(3x+1/x)²=10²__(3x)²+2(3x)(1/x)+(1/x)²=100_______________9x²+6+1/x²=100_________________9x²+1/x²=94 [A] 5. a³+b³=(a+b)(a²-ab+b²)=(1)[(a²+b²)-(-3)]=(a²+2ab+b²-2ab)+3=[(a+b)²-2(-3)]+3=[(1)²+6]+3=10 [D]

2011-12-30 11:59:58 補充：
(√3+2)×(2-√3)²ºº⁹+²º¹º
=(√3+2)×(2-√3)²ºº⁹×(2-√3)²º¹º
=/=(√3+2)²ºº⁹×(2-√3)²º¹º !!!
[(√3+2)×(2-√3)²ºº⁹=/=(√3+2)²ºº⁹]

(A^a) x (A^b) = A^(a+b)
(√3+2) is not equal to (2-√3)

(A^a) x (B^a) = (AB)^a