Solve each of the following equations using the method of taking square roots.[1](Leave the answers in surd form.)
[2](Give the answers correct to 2 decimal places.)
1.4[1-(1/3)x]^2 -5=0
2.1.5-0.2(x-1/2)^2=0
Solve the following equation using the quadratic formula.(Give the answers correct to 2 decimal places.)
3.(2/3)x^2 -(5/9)x - 1/3=0
Solve each of the following equarions using any method.(Leave the answers in surd form if necessary, and identify those equations that have no real roots.)
4. -8(2x+1)(2x+1)= -64
5. 4(x-0.1)^2 = (2x-0.3)^2
Quadratic equations( F.4)
2009-04-30 5:07 am
回答 (1)
2009-05-01 9:14 am
✔ 最佳答案
1.4[1 - (1/3)x]2 - 5 = 0
[1 - (1/3)x]2 = 5/4
[(1/3)x - 1]2 = 5/4
(1/3)x - 1 = √(5/4) ..or.. (1/3)x - 1 = -√(5/4)
(1/3)x - 1 = (√5)/2 ..or.. (1/3)x - 1 = -(√5)/2
(1/3)x = (2 + √5)/2 ..or.. (1/3)x = (2 - √5)/2
[1].. x = (6 + 3√5)/2 ..or.. x = (6 - 3√5)/2
[2].. x = 6.35 ..or.. x = -0.35
2.
1.5 - 0.2(x - 1/2)2 = 0
0.2(x - 1/2)2 = 1.5
(x - 1/2)2 = 1.5/0.2
(x - 1/2)2 = 30/4
x - 1/2 = √(30/4) ..or.. x - 1/2 = -√(30/4)
x - 1/2 = (√30)/2 ..or.. x - 1/2 = -(√30)/2
[1].. x = (1 + √30)/2 ..or.. x = (1 - √30)/2
[2].. x = 3.24 ..or.. x = -2.24
3.
(2/3)x2 - (5/9)x - (1/3) = 0
9[(2/3)x2 - (5/9)x - (1/3)] = 0
6x2 - 5x - 3 = 0
x = {-(-5) + √[(-5)2 - 4(6)(-3)]}/(2 x 6) ..or.. x = {-(-5) - √[(-5)2 - 4(6)(-3)]}/(2 x 6)
x = (5 + √97)/12 ..or.. x = (5 - √97)/12
x = 1.24 ..or.. x = -0.40
4.
-8(2x + 1)(2x + 1) = -64
(2x + 1)2 = 8
2x + 1 = √8 ..or.. 2x + 1 = -√8
2x + 1 = 2√2 ..or.. 2x + 1 = -2√2
2x = -1 + 2√2 ..or.. 2x = -1 -2√2
x = (-1 + 2√2)/2 ..or.. x = (-1 -2√2)/2
5.
4(x - 0.1)2 = (2x - 0.3)2
4(x2 - 0.2x + 0.01) = 4x2 - 1.2x + 0.09
4x2 - 0.8x + 0.04 = 4x2 - 1.2x + 0.09
0.4x = 0.05
x = 0.125
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