solve quadratic equation using an appropriate method ,,leave your answers in surd form if necessary
3 ( x^2-1) = 2x/3
計極都計唔到
2007-10-29 8:15 am
回答 (5)
2007-10-29 8:28 am
✔ 最佳答案
3 ( x^2-1) = 2x/3 Multiply both sides by 3,
9 (x^2 - 1) = 2x
9x^2 - 9 = 2x
9x^2 - 2x - 9 = 0
By using the quadratic formula,
x = {-(-2) ± √[(-2)^2-4(9)(-9)] } / [(2)(9)]
= {2 ± √(4 + 324)} / 18
= [2 ± √(328)] / 18
= [2 ± 2√(82)] / 18
= [1 ± √(82)] / 9
If there is a mistake, please inform me.
參考: My Maths knowledge
2007-10-31 2:39 am
3(x^2-1)=2x/3
3x^2-3=2x/3
3(3x^2-3)=2x
9x^2-2x-9=0
∴ {2±√[(-2)^2-(4)(9)(-9)}/2*9
=[2±√(4+324)]/18
=(2±√328)/18
=(2±2√82)/18
=(1±√82)/18
3x^2-3=2x/3
3(3x^2-3)=2x
9x^2-2x-9=0
∴ {2±√[(-2)^2-(4)(9)(-9)}/2*9
=[2±√(4+324)]/18
=(2±√328)/18
=(2±2√82)/18
=(1±√82)/18
2007-10-29 10:41 pm
3 ( x^2-1) = 2x/3
=> 9 (x^2 - 1) = 2x by multiplying 3 on both sides
=> 9x^2 - 2x - 9 = 0 by adding 2x on both sides
Then, discriminant, d = [(-2)^2 - 4(9)(-9)]^(1/2) = [2^2 x (1 + 81)]^(1/2) = 2x(82)^(1/2)
By quadratic formula,
x = [-(-2) + d]/(2x9) or [-(-2) - d]/(2x9) = [1 + 82^(1/2)]/9 or [1 - 82^(1/2)]/9
=> 9 (x^2 - 1) = 2x by multiplying 3 on both sides
=> 9x^2 - 2x - 9 = 0 by adding 2x on both sides
Then, discriminant, d = [(-2)^2 - 4(9)(-9)]^(1/2) = [2^2 x (1 + 81)]^(1/2) = 2x(82)^(1/2)
By quadratic formula,
x = [-(-2) + d]/(2x9) or [-(-2) - d]/(2x9) = [1 + 82^(1/2)]/9 or [1 - 82^(1/2)]/9
2007-10-29 10:45 am
3 ( x^2-1) = 2x/3
3x^2 - 3 = 2x/3
3 (3x^2 - 3) = 2x
9x^2 - 9 = 2x
9x^2 - 2x -9 = 0
x= [-b + √(b^2 -4ac)] / 2a
x=2 + √[4 - 4(9)(-9)]/2(9)
x=(2+ √328)/18 or x = (2- √328)/18
3x^2 - 3 = 2x/3
3 (3x^2 - 3) = 2x
9x^2 - 9 = 2x
9x^2 - 2x -9 = 0
x= [-b + √(b^2 -4ac)] / 2a
x=2 + √[4 - 4(9)(-9)]/2(9)
x=(2+ √328)/18 or x = (2- √328)/18
2007-10-29 8:32 am
3 ( x^2-1) = 2x/3
=> 9x^2 - 9 = 2x
=> 9x^2 - 2x - 9 = 0
using quadratic formula,
x = (2 +/- sqrt(328)) / 18 = (2 +/- 2 * sqrt(82)) / 18 = (1 +/- sqrt(82)) / 9
=> 9x^2 - 9 = 2x
=> 9x^2 - 2x - 9 = 0
using quadratic formula,
x = (2 +/- sqrt(328)) / 18 = (2 +/- 2 * sqrt(82)) / 18 = (1 +/- sqrt(82)) / 9
收錄日期: 2021-04-13 14:14:21
原文連結 [永久失效]:
https://hk.answers.yahoo.com/question/index?qid=20071029000051KK00062