英文數學工課急要高手幫忙,急要答案

5.
x² - 5x - 3 = 0
x = {-(-5) ± √[(-5)² - 4(1)(-3)]} / 2(1)
x = (5 ± √37)/2
x = 5.54 or x = -0.54


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6.
x² - 10x + 5 = 0
x = {-(-10) ± √[(-10)² - 4(1)(5)]} / 2(1)
x = (10 ± 4√5)/2
x = 5 ± 2√5
x = 9.47 or x = 0.53


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7.
3x² - 6x + 2 = 0
x = {-(-6) ± √[(-6)² - 4(3)(2)] / 2(3)
x = (6 ± 2√3)/6
x = (3 ± √3)/3
x = 1.58 or x = 0.42


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8.
2x² - x + 3 = 0
x = {-(-1) ± √[(-1)² - 4(2)(3)]} / 2(2)
x = [1 ± (√23)i]/4
x = 0.25 + 1.20i or 0.25 - 1.20i


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9.
Let n and (n + 1) be the two integers.

n² + (n + 1)² = 85
n² + n² + 2n + 1 = 0
2n² + 2n - 84 = 0
n² + n - 42 = 0
n = {-1 ± √[1² - 4(1)(-42)]} / 2(1)
n = (-1 ± 13)/2
n = 6 or x = -7

The two consecutive positive integer = 6, 7


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10.
By Pythagorean theorem :
x² + (2x + 2)² = 13²
x² + 4x² + 8x + 4 = 169
5x² + 8x - 165 = 0

x = {-8 ± √[8² - 4(5)(-165)]} / 2(5)
x = (-8 ± √3364)/10
x = 5 or x = -6.6