1.The difference of two positive integers is 5.Two times the square of the smaller one exceeds the square of the larger one by 71.Find the two integers.
2.The true bearing and compass bearing of a ship from a lighthouse are x(x+2)∘and S(3x+2)∘W respectively.Find the value of x.
Quadratic Equations*2
2011-09-26 3:30 am
回答 (3)
2011-09-26 3:41 am
✔ 最佳答案
1 Let the two numbers are x and yx - y = 5, 2y^2 - x^2 = 71
So, 2y^2 - (y + 5)^2 = 71
y^2 - 10y - 96 = 0
(y - 16)(y + 6) = 0
y = 16, x = 21
2 x(x + 2) = 180 + 3x + 2
x^2 - x - 182 = 0
(x - 14)(x + 13) = 0
x= -13 (rejected) or x = 14
2011-09-26 5:26 am
For Q2.
Since the true bearing is counting from North in clockwise direction and the compass bearing is counting from South, there is a difference of 180 degree.
So x(x + 2) = 180 + 3x + 2
x^2 + 2x = 3x + 182
x^2 - x - 182 = 0
(x + 13)(x - 14) = 0
x = - 13 (reject) or 14.
So the true bearing is 14(16) = 224 degree, that is S44W which is S [3(14) + 2]W.
Since the true bearing is counting from North in clockwise direction and the compass bearing is counting from South, there is a difference of 180 degree.
So x(x + 2) = 180 + 3x + 2
x^2 + 2x = 3x + 182
x^2 - x - 182 = 0
(x + 13)(x - 14) = 0
x = - 13 (reject) or 14.
So the true bearing is 14(16) = 224 degree, that is S44W which is S [3(14) + 2]W.
2011-09-26 4:50 am
2.
x(x+2)=180+(3x+2)
x^2+2x-182-3x=0
...
so try it...
x(x+2)=180+(3x+2)
x^2+2x-182-3x=0
...
so try it...
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