中X數學題

1. 18/(10-x) + 28/(10+x) = 5
180 + 18x + 280 - 28x = 500 - 5x^2
5x^2 - 10x - 40 = 0
x^2 - 2x - 8 = 0
(x-4)(x+2) = 0
x = 4 or -2

2.(3x+2)^2+(4x-1)^2>(5x+1)^2 for x
(3x+2)^2+(4x-1)^2>(5x+1)^2
9x^2 + 12x + 4 + 16x^2 - 8x + 1 > 25x^2 + 10x + 1
-6x + 4 > 0
6x < 4
x < 2/3

3.A rectangle has an area of 48 cm^2 and a perimeter of 28 cm . Find the length and width of the rectangle.
Let x cm be the length, i.e. width = (48/x)cm
2(x + 48/x) = 28
x + 48/x = 14
x^2 - 14x + 48 = 0
(x - 8)(x-6) = 0
x = 8 or 6
Length = 8cm when width = 6cm;
Length = 6cm when width = 8cm

4.x and y are two consective integers. x and y are the tens digit and units digit of a two-digit number . The product of the digits is 12 . the value of the number is increased by 9 when the digits are reversed . Find the two-digit number.
xy = 12 --------------(1)
10x+y + 9 = 10y + x
9x - 9y = -9
x - y = -1
x = y - 1------------(2)
Sub (2) into (1)
y(y-1) = 12
y^2 - y - 12 = 0
(y - 4)(y + 3) = 0
y =4 or -3 (rej.)
Sub y = 4 into (2)
x = 4 - 1 = 3
Hence, the number = 34