1.the sum of positive integer and its square is 56.find the integer
2.the figure shows a rectangle of length x cm.if the perimeter and the are of the rectangle are 60 cm and 216 cm2 respectively,find the value of x.
3.the dimensions of a rectangular cardboard are 26 cm X 16 cm.A square of side x cm is cut away from each corner of the cardboard.the remaining part is folded up to form an open box.
(A)express the base area of the open box in terms of x.
(B)if the base of area of the box is 200 cm2.find the volume of the box.
4.the square of the sum of three consecutive positive integers is greater than the sum of their squares by 94.find the three integers.
f.4一元二次方程(I)(10分)
2014-09-26 5:17 am
回答 (2)
2014-09-26 10:32 am
✔ 最佳答案
1.Let n be the positive integer.
n + n² = 56
n² + n - 56 = 0
(n - 7)(n + 8) = 0
n = 7 or n = 8 (rejected)
The integer is 7.
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2.
The width of the rectangle = (60 - 2x)/2 cm = (30 - x) cm
The area of the rectangle (in cm²) :
x(30 - x) = 216
30x - x² = 216
x² - 30x + 216 = 0
(x - 18)(x - 12) = 0
x = 18 or x = 12 (rejected,if condition that "length greater than width" holds)
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3.
(A)
Base area of the box
= (26 - 2x)(16 - 2x) cm²
(B)
(26 - 2x)(16 - 2x) = 200
416 - 84x + 4x² = 200
4x² - 84x + 216 = 0
x² - 21x + 54 = 0
(x - 3)(x - 18) = 0
x = 3 or x = 18 (rejected)
Volume of the box
= 200 * 3 cm³
= 600 cm³
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4.
Let (n - 1), n and (n + 1) be the three consecutive positive integers.
[(n - 1) + n + (n + 1)]²- [(n - 1)² + n² + (n + 1)²] = 94
[3n]² - [n² - 2n + 1 + n² + n² + 2n + 1] = 94
9n² - 3n² - 2 = 94
6n² - 96 = 0
6(n - 4)(n + 4) = 0
n = 4 or n = -4 (rejected)
The three integers are 3, 4 and 5.
2014-09-26 02:33:17 補充：
發問時點數已扣除，刪除問題只會損人不利己。
2014-09-26 03:27:35 補充：
大家也未睡，大家也應保重。
參考: 土扁, 土扁
2014-09-26 10:35 am
土扁師兄，那麼夜還不睡～
保重～
保重～
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