✔ 最佳答案
1.
設紅色彈珠有 2k 枚,綠色彈珠有 5k枚。
5k - 2k = 27
k = 9
紅色彈珠的數量
= 2k 枚
= 18 枚
2.
a)
x - y = 3
y = x - 3
z - y = 6
y = z - 6
故聯立方程式可重寫為:
y = x - 3
y = z - 5
x + z = 6
b)
y = x - 3 ... [1]
y = z - 5 ... [2]
x + z = 6 ... [3]
[1] + [2] + [3] :
2y + x + z = x + z - 2
y = -1
把 y = -1 代入[1] 中:
-1 = x - 3
x = 2
把 y = -3/2 代入 [2]中:
-1 = z - 5
z = 4
=====
1)
4√3 - √12
4√3 - √(2²*3)
= 4√3 - 2√3
= 2√3
=====
2)
3√90 + 2√40
= 3√(3²*10) + 2√(2²*10)
= 9√10 + 4√10
= 13√10
=====
3)
6√20 - √125 + 2√45
= 6√(2²*5) - √(5³) +2√(3²*5)
= 12√5 - 5√5 + 6√5
= 13√5
=====
4)
6√28 + 2√175 - 3√343
= 6√(2²*7) + 2√(5²*7)- 3√(7³)
= 12√7 + 10√7 - 21√7
= √7
=====
5)
(√5 - √3)(√5 + √3)
= (√5)² - (√3)²
= 5 - 3
= 2
====
6)
(3√2 + √13)(3√2 - √13)
= (3√2)² - (√13)²
= 18 - 13
= 5
=====
7)
(√7 + √3)²
= (√7)² + 2(√7)( √3) + (√3)²
= 7 + 2√21 + 3
= 10 + 2√21
=====
8)
(2√6 - 3√2)²
= (2√6)² - 2(2√6)(3√2) + (3√2)²
= 24 - 12√(2²*3) + 18
= 42 - 24√3