Question

solve for x , (2x / x-4 )^2 - (2x/ x-4) -24 =0​

Answer 1

Given;

${(\frac{2x}{x - 4} )}^{2} - \: (\frac{2x}{x - 4} ) \: - 24 \: = 0$

$let \: {(\frac{2x}{x - 4} )} \: = a$

Then the eq. would be

• a² - a - 24 = 0

By using quadratic formula ;

• D or d = (-1)² - 4(-24)(1)
• d = 1 + 96
• d = 97

Thus the roots α & β using quadratic formula can be given by ;

$\alpha = \frac{ \: - b \: + \sqrt{d} }{2a}$

$\alpha \: = \frac{ \: - ( - 1) \: + \sqrt{97} }{2(1)}$

$\alpha = \frac{ \: 1 \: + \sqrt{97} }{2}$

$\beta \: = \frac{ \: - b \: - \sqrt{d} }{2a}$

$\beta \: = \frac{ \: - ( - 1) \: - \sqrt{97} }{2(1)}$

$\beta = \frac{ \: 1 \: - \sqrt{97} }{2}$

Thus value of a = (2x/x-4) can be either α or β.

#answerwithquality

#BAL