Question

Solve for x: (2x/x-5)²+(2x/x-5)-24=0 , x≠5

Answer 1

x = 5 (√97 + 1)/(√97 + 5), 5 (√97 - 1)/(√97 - 5)

Step-by-step explanation:

The given equation is

{2x/(x - 5)}² + 2x/(x - 5) - 24 = 0, where x ≠ 5

or, a² + a - 24 = 0, where 2x/(x - 5) = 0

or, a² + (2 * a * 1/2) + (1/2)² - 24 - (1/2)² = 0

or, (a + 1/2)² - (24 + 1/4) = 0

or, (a + 1/2)² - {(√97)/2}² = 0

or, {a + 1/2 + (√97)/2} {a + 1/2 - (√97)/2} = 0

Either a + 1/2 + (√97)/2 = 0 or, a + 1/2 - (√97/2) = 0

Taking the first value of a, we get

2x/(x - 5) + 1/2 + (√97)/2 = 0

or, 2x/(x - 5) = - 1/2 * (1 + √97)

or, 4x = - (1 + √97) (x - 5)

or, (4 + 1 + √97)x = 5 (1 + √97)

or, x = 5 (√97 + 1)/(√97 + 5)

Again taking the second value of a, we get

2x/(x - 5) + 1/2 - (√97)/2 = 0

or, 2x/(x - 5) = - 1/2 * (1 - √97)

or, 4x = - (1 - √97) (x - 5)

or, (4 + 1 - √97)x = 5 (1 - √97)

or, x = 5 (√97 - 1)/(√97 - 5)

Therefore the required solution is

x = 5 (√97 + 1)/(√97 + 5), 5 (√97 - 1)/(√97 - 5)

Note: If you can want, you may rationalise the denominators.

Related question here:

Solve the following quadratic equation x² -7x + 3 = 0. Give your answer correct to two decimal places. - https://brainly.in/question/15750559

Answer 2

Step-by-step explanation:

above is correct ...

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