匿名使用者
匿名使用者 發問時間: 科學數學 · 8 年前

2 maths question(S.2)

express the following numbers in the form of the fraction a/b

.

0.1

..

1.16

.

-0.12

what is the consecutive integers where 根203 is in between?

---------------------------

(3根5 - 根3) (2根3 + 4根5)

(根5 - 根2) (根5 + 根2)

1 個解答

評分
  • 8 年前
    最佳解答

    express the following numbers in the form of the fraction a/b

    .

    0.1=1/10

    ..

    1.16=116/100=29/25

    ...

    -0.12=-12/100=-3/25

    what is the consecutive integers where 根203 is in between?

    Because the square of 14 equals 196, and the square of 15 equals 225, we can know that  radical sign of 203 is between 14 and 15.

    (3根號5-根號3)(2根號3+4根號5)

    =3根號5*2根號3+3根號5*4根號5-根號3*2根號3-根號3*4根號5

    =6根號15+12*5-2*3-4根號15

    =54+2根號15

    (根號5-根號2)(根號5+根號2)

    =(根號5)^2-(根號2)^2

    =5-2=3

    若看不懂請反應,我會補上中文解答

    2012-08-14 20:31:18 補充:

    請以a/b這種分數的形式表示以下題目

    .

    0.1=1/10

    ..

    1.16=116/100

    ...

    -0.12=-12/100=-3/25

    2012-08-14 20:36:15 補充:

    請問√203是介於哪兩個連續數字之間?

    因為14的平方是196,15的平方是225,所以√203是介於14和15之間

    (補充:因為196<203<225

    √196<√203<√225

    √(14^2)<√203<√(15^2)

    所以14<√203<15)

    2012-08-14 20:41:11 補充:

    (3√5-√3)(2√3+4√5)

    =3√5*2√3+3√5*4√5-√3*2√3-√3*4√5

    =6√15+12*5-2*3-4√15

    =54+2√15

    (√5-√2)(√5+√2)

    =(√5)^2-(√2)^2

    =5-2=3

    (補充公式:(a+b)(a-b)=a^2-b^2

    證明:

    (a+b)(a-b)

    =a*a+a*(-b)+b*a+b*(-b)

    =a^2-ab+ab-b^2

    =a^2-b^2)

    參考資料: ありがとうございます
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