Maths~

1. (1+20/x)(8/x-1)=3
8/x-1+160/(x^2) -20/x =3
160/(x^2) - 12/x = 4
160 - 12x = 4x^2 (將成條式乘x^2)
x^2 +3x-40 = 0
(x+8)(x-5) = 0
x = -8 or +5


2.3/(x+3)+2/x= - 4/3
9x/3x(x+3) + 6(x+3)/3x(x+3) = -4x(x+3)/3x(x+3) (將分母變做 3x(x+3))
9x + 6(x+3) = -4x(x+3)
9x+6x+18 = -4x^2-12x
4x^2 +27x+18= 0
(x+6)(4x+3) = 0
x = -6 or -3/4

3. 14- 24x + 5x^2 = 50
5x^2 - 24x -36 = 0
(5x+6)(x-6) = 0
x = -5/6 or +6

4.(a) x-7
(b) (x)(x+7) = 450
x^2 + 7x = 450
x^2 +7x -450 = 0
x = 18 or -25

5. Let x be the no. of calculators bought
[Cost of each calculator = $4600/x]
** [(4600/x)+40](x-4) = 4600+980
[(4600+40x)/x ](x-4) = 5580
4600+40x - [(18400+160x)/x] = 5580
-980 + 40x -[(18400+160x)/x] = 0
40x^2 -980x -18400 -160x =0
40x^2 -1140x -18400 = 0
2x^2 - 57x - 920 = 0
x = 40 or -11.5(rejected)

Cost of each calculator = $4600/40 = $115

6. Let x% be the annual interest
1000 ( 1+ x/12)^2 = 2030.1
(1+x/12)^2 = 2.0301
(1+x/12) = 1.4248
x/12 = 0.4248
x = 5.10
Annual interest = 5.10 %


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