# Please check my working out

• Jun 8th 2009, 06:24 AM
Joel
Hi all,

Given this question and was hoping you can check my working out.

Find x in terms of c, given that (2 / 3x-2c) + (3 / 2x-3c) = (7 / 2c)

4c(2x-3c) + 6c(3x-2c) = 7(3x-2c)(2x-3c)
8xc – 12c² + 18xc – 12c² = 7(6x² - 9xc – 4xc + 6c²)
8xc – 12c² + 18xc – 12c² = 42x² - 91xc + 42c²
42x² - 117xc + 76c² = 0
x = 117c ± √(117c)² - 4 (42)(76c²)
2(42)
x = 117c ± √(117c)² - 12768
84
x = 117c ± √921c²
84

Cheers
• Jun 8th 2009, 06:55 AM
Amer
Quote:

Originally Posted by Joel
Hi all,

Given this question and was hoping you can check my working out.

Find x in terms of c, given that (2 / 3x-2c) + (3 / 2x-3c) = (7 / 2c)

$\displaystyle 4c(2x-3c) + 6c(3x-2c) = 7(3x-2c)(2x-3c)$

$\displaystyle 8xc - 12c^2 + 18xc -12c^2 = 7(6x^2 - 9xc - 4xc + 6c^2)$

$\displaystyle 8xc- 12c^2 + 18xc - 12c^2 = 42x² - 91xc + 42c^2$

$\displaystyle 42x^2 - 117xc +{\color{red} 76}c^2 = 0$

x = 117c ± √(117c)² - 4 (42)(76c²)
2(42)
x = 117c ± √(117c)² - 12768
84
x = 117c ± √921c²
84

Cheers

$\displaystyle 4c(2x-3c) + 6c(3x-2c) = 7(3x-2c)(2x-3c)$

$\displaystyle 8xc - 12c^2 + 18xc -12c^2 = 7(6x^2 - 9xc - 4xc + 6c^2)$

$\displaystyle 8xc- 12c^2 + 18xc - 12c^2 = 42x^2 - 91xc + 42c^2$

$\displaystyle 42x^2 - 117xc + {\color{red}76}c^2 = 0$

$\displaystyle {\color{blue}42x^2 - 117xc +66c^2 = 0}$

$\displaystyle x=\frac{117\pm \sqrt{13689c^2-11088c^2}}{84}$

$\displaystyle x=\frac{117\pm \sqrt{2601c^2}}{84}$

$\displaystyle x=\frac{117\pm 51c}{84}$
• Jun 8th 2009, 07:00 AM
Joel
what a difference 10 can make. lol

Thanks heaps