Yahoo Answers: Answers and Comments for Find all solutions to x^39x^24=0 to two decimal places?
please show step by step.? [Mathematics]
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From Oziel
enGB
Mon, 19 Aug 2019 04:31:30 +0000
3
Yahoo Answers: Answers and Comments for Find all solutions to x^39x^24=0 to two decimal places?
please show step by step.? [Mathematics]
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From Austin: You're answer would be 9.05
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Mon, 19 Aug 2019 04:40:41 +0000
You're answer would be 9.05

From ted s: comment : there is only one real root , not ra...
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Mon, 19 Aug 2019 04:39:26 +0000
comment : there is only one real root , not rational , close to 9.05...you can use Newton's methods to approximate the value...start at x = 9

From Captain Matticus, LandPiratesInc: There's only one real solution
https://ww...
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Mon, 19 Aug 2019 04:54:54 +0000
There's only one real solution
https://www.wolframalpha.com/input/?i=x%5E3++9x%5E2++4+%3D+0
You can solve it using various methods
https://en.wikipedia.org/wiki/Cubic_function#General_solution_to_the_cubic_equation_with_real_coefficients
ax^3 + bx^2 + cx + d = 0
a = 1 , b = 9 , c = 0 , d = 4
p = b^2  3ac = 81  3 * 1 * 0 = 81
q = 2b^3  9abc + 27a^2 * d = 2 * (9)^3  9 * 1 * (9) * 0 + 27 * 1^2 * (4) = 2 * (729)  108 = 1458  108 = 1566
C^3 = ((q +/ sqrt(q^2  4p^3)) / 2)
C^3 = ((1566 +/ sqrt(1566^2  4 * 81^3)) / 2)
C^3 = ((1566 +/ sqrt(9^2 * 174^2  4 * 9^6)) / 2)
C^3 = ((1566 +/ sqrt(9^2 * 9 * 58^2  4 * 9^6)) / 2)
C^3 = ((1566 +/ sqrt(9^3 * (58^2  4 * 9^3))) / 2)
C^3 = ((1566 +/ sqrt(3^6 * (4 * 29^2  4 * 9^3))) / 2)
C^3 = ((1566 +/ 3^3 * 2 * sqrt(29^2  9^3))) / 2)
C^3 = ((1566 +/ 54 * sqrt(841  729)) / 2)
C^3 = 783 +/ 27 * sqrt(112)
C^3 = 783 +/ 27 * 4 * sqrt(7)
C^3 = 27 * 29 +/ 27 * 4 * sqrt(7)
C^3 = 27 * (29 +/ 4 * sqrt(7))
C = 3 * (29 +/ 4 * sqrt(7))^(1/3)
x = (1/(3a)) * (C + p/C)
x = (1/3) * (3 * (29 +/ 4 * sqrt(7))^(1/3) + 81 / (3 * (29 +/ 4 * sqrt(7))^(1/3)))
x = (1/3) * (3 * (29 +/ 4 * sqrt(7))^(1/3) + 27 / (29 +/ 4 * sqrt(7))^(1/3))
x = (1) * ((29 +/ 4 * sqrt(7))^(1/3) + 9 * (29 +/ 4 * sqrt(7))^(2/3) / (29 +/ 4 * sqrt(7)))
Are you done looking at this hell yet?

From Krishnamurthy: x^39x^24=0
Real solution:
x = 3 + (29  4 sq...
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Mon, 19 Aug 2019 06:42:25 +0000
x^39x^24=0
Real solution:
x = 3 + (29  4 sqrt(7))^(1/3) + (29 + 4 sqrt(7))^(1/3)
Complex solutions:
x ≈ 0.02443  0.66442 i
x ≈ 0.02443 + 0.66442 i