1.Let a,b be the roots of the equation x^2 + px + q = 1 .........(＊) where p and q are real constants.
Find, in terms of p and q,
(a) ( a^2 - b - 1)(b^2 - a - 1)
(b) If the square of one roots of (＊) minus the other root equals 1,use (a) or otherwise ,to show that q^2 - 3(p - 1)q + ( p -1 )^2( p + 1 ) = 0 ..........(＊＊).
Quadratic equation
2007-01-12 3:19 am
回答 (3)
2007-01-12 3:45 am
✔ 最佳答案
1. The length and the width of a rectangle are x cm and y cm respectively.a) The perimeter of the rectangle is 68 cm.
Write down an equation in x and y.
2(x + y) = 68
x + y = 34 -----(1)
b) Suppose its length is increased by 4cm and its width is decreased by 4cm.
i) Find, in terms of x and y, the new area of the rectangle.
new area = (x + 4)(y – 4)
ii)Find its original dimensions if the new area is reduced by 40 cm2.
xy - (x + 4)(y – 4) = 40
xy – xy + 4x – 4y +16 = 40
4x – 4y = 24
x – y = 6 -----(2)
(1)式加(2)式
2x = 40
x = 20cm
y = 30 – 6 = 14cm
所以這長方形的大小為 20cm * 14cm
面積是 280cm2
2007-01-12 6:01 am
I think the answer shoud be 280
2007-01-12 4:20 am
1. The length and the width of a rectangle are x cm and y cm respectively.
a) The perimeter of the rectangle is 68 cm.
Write down an equation in x and y.
2(x + y) = 68
x + y = 34 -----(1)
b) Suppose its length is increased by 4cm and its width is decreased by 4cm.
i) Find, in terms of x and y, the new area of the rectangle.
new area = (x + 4)(y – 4)
ii)Find its original dimensions if the new area is reduced by 40 cm2.
xy - (x + 4)(y – 4) = 40
xy – xy + 4x – 4y +16 = 40
4x – 4y = 24
x – y = 6 -----(2)
(1)式加(2)式
2x = 40
x = 20cm
y = 30 – 6 = 14cm
所以這長方形的大小為 20cm * 14cm
面積是 280cm2
a) The perimeter of the rectangle is 68 cm.
Write down an equation in x and y.
2(x + y) = 68
x + y = 34 -----(1)
b) Suppose its length is increased by 4cm and its width is decreased by 4cm.
i) Find, in terms of x and y, the new area of the rectangle.
new area = (x + 4)(y – 4)
ii)Find its original dimensions if the new area is reduced by 40 cm2.
xy - (x + 4)(y – 4) = 40
xy – xy + 4x – 4y +16 = 40
4x – 4y = 24
x – y = 6 -----(2)
(1)式加(2)式
2x = 40
x = 20cm
y = 30 – 6 = 14cm
所以這長方形的大小為 20cm * 14cm
面積是 280cm2
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