simplify
1. 4/(3-√5) -1/(√2+1)
2. (4(√3+1))/(√3+1) – (2-√3)/(2+√3)
3. 6/(2√3-3√2)-√2/(3+√6)
rationalize denominators
4. (√3-4)/((1+√3)(√3-2))
5.(√a+a)/(a+√a+1)
求數學高手解答! MATHS QUESTIONS!?
2015-12-13 3:01 am
回答 (2)
2015-12-13 3:35 am
1. 4/(3-√5) -1/(√2+1)=4(3+√5)/[(3-√5)(3+√5)] -1(√2-1)/[(√2+1)(√2-1)]
=4(3+√5)/4 -1(√2-1)/1=(3+√5)-(√2-1)=4+√5-√2
2. (4(√3+1))/(√3+1) – (2-√3)/(2+√3)=4– (2-√3)(2-√3)/(2+√3)(2-√3)
=4– (4-4√3+3)/1=4– (7-4√3)=4√3-3
3. 6/(2√3-3√2)-√2/(3+√6)=6(2√3+3√2)/(2√3-3√2)(2√3+3√2)-√2(3-√6)/(3+√6)(3-√6)
=6(2√3+3√2)/6-√2(3-√6)/3=2√3+3√2-(3√2-2√3)/3=2√3+3√2-√2+2√3/3=2√2 + 8√3/3
4. (√3-4)/((1+√3)(√3-2))=(√3-4)/(√3-2+3-2√3)=(√3-4)/(1-√3)
=(√3-4)(1+√3)/(1-√3)(1+√3)=(√3+3-4-4√3)/(-2)=(-1-3√3)/(-2)=(1+3√3)/2
5.(√a+a)/(a+√a+1)=(√a+a)(a+1-√a)/(a+1+√a)(a+1-√a)=(a√a+√a-a+a^2+a-a√a)/[(a+1)^2-a]
=(a^2+√a)/(a^2+a+1)
=4(3+√5)/4 -1(√2-1)/1=(3+√5)-(√2-1)=4+√5-√2
2. (4(√3+1))/(√3+1) – (2-√3)/(2+√3)=4– (2-√3)(2-√3)/(2+√3)(2-√3)
=4– (4-4√3+3)/1=4– (7-4√3)=4√3-3
3. 6/(2√3-3√2)-√2/(3+√6)=6(2√3+3√2)/(2√3-3√2)(2√3+3√2)-√2(3-√6)/(3+√6)(3-√6)
=6(2√3+3√2)/6-√2(3-√6)/3=2√3+3√2-(3√2-2√3)/3=2√3+3√2-√2+2√3/3=2√2 + 8√3/3
4. (√3-4)/((1+√3)(√3-2))=(√3-4)/(√3-2+3-2√3)=(√3-4)/(1-√3)
=(√3-4)(1+√3)/(1-√3)(1+√3)=(√3+3-4-4√3)/(-2)=(-1-3√3)/(-2)=(1+3√3)/2
5.(√a+a)/(a+√a+1)=(√a+a)(a+1-√a)/(a+1+√a)(a+1-√a)=(a√a+√a-a+a^2+a-a√a)/[(a+1)^2-a]
=(a^2+√a)/(a^2+a+1)
2015-12-13 9:23 am
1. 4/(3-√5) -1/(√2+1)=4(3+√5)/[(3-√5)(3+√5)] -1(√2-1)/[(√2+1)(√2-1)]
=4(3+√5)/4 -1(√2-1)/1=(3+√5)-(√2-1)=4+√5-√2
2. (4(√3+1))/(√3+1) – (2-√3)/(2+√3)=4– (2-√3)(2-√3)/(2+√3)(2-√3)
=4– (4-4√3+3)/1=4– (7-4√3)=4√3-3
3. 6/(2√3-3√2)-√2/(3+√6)=6(2√3+3√2)/(2√3-3√2)(2√3+3√2)-√2(3-√6)/(3+√6)(3-√6)
=6(2√3+3√2)/6-√2(3-√6)/3=2√3+3√2-(3√2-2√3)/3=2√3+3√2-√2+2√3/3=2√2 + 8√3/3
4. (√3-4)/((1+√3)(√3-2))=(√3-4)/(√3-2+3-2√3)=(√3-4)/(1-√3)
=(√3-4)(1+√3)/(1-√3)(1+√3)=(√3+3-4-4√3)/(-2)=(-1-3√3)/(-2)=(1+3√3)/2
5.(√a+a)/(a+√a+1)=(√a+a)(a+1-√a)/(a+1+√a)(a+1-√a)=(a√a+√a-a+a^2+a-a√a)/[(a+1)^2-a]
=(a^2+√a)/(a^2+a+1)
=4(3+√5)/4 -1(√2-1)/1=(3+√5)-(√2-1)=4+√5-√2
2. (4(√3+1))/(√3+1) – (2-√3)/(2+√3)=4– (2-√3)(2-√3)/(2+√3)(2-√3)
=4– (4-4√3+3)/1=4– (7-4√3)=4√3-3
3. 6/(2√3-3√2)-√2/(3+√6)=6(2√3+3√2)/(2√3-3√2)(2√3+3√2)-√2(3-√6)/(3+√6)(3-√6)
=6(2√3+3√2)/6-√2(3-√6)/3=2√3+3√2-(3√2-2√3)/3=2√3+3√2-√2+2√3/3=2√2 + 8√3/3
4. (√3-4)/((1+√3)(√3-2))=(√3-4)/(√3-2+3-2√3)=(√3-4)/(1-√3)
=(√3-4)(1+√3)/(1-√3)(1+√3)=(√3+3-4-4√3)/(-2)=(-1-3√3)/(-2)=(1+3√3)/2
5.(√a+a)/(a+√a+1)=(√a+a)(a+1-√a)/(a+1+√a)(a+1-√a)=(a√a+√a-a+a^2+a-a√a)/[(a+1)^2-a]
=(a^2+√a)/(a^2+a+1)
收錄日期: 2021-04-18 14:10:56
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