Question

Solve 3sqrt(x) = 8/(sqrt(9x - 32)) + sqrt(9x - 32)​

Answer 1

`\huge \color{gray}{ \tt{answer}}`

`x = 4`

Explanation:

`3 √(x) = (8)/((9x - 32)) + √((9x - 32))`

• move the expression to the left

`3 √(x) - (8)/( √(9x - 32) ) - √(9x - 32) = 0`

• transform the expression

`(3 √((9x - 32 x)) - 8 - √(9x - 32) )/( √(9x - 32) )`

• set the numerator

`3 √((9x - 32)x) - 8 - (9x - 32) = 0`

• remove the parentheses

`3 \sqrt{9 {x}^(2) - 32x} + 24 - 9x = 0`

• move the expression to the right

`3 \sqrt{9 {x}^(2) - 32x } - 24 + 9x`

• divide both sides

`\sqrt{9 {x}^(2) - 32x } = - 8 + 3x`

• simplify the expression

`9 {x}^(2) - 32x = 9 {x}^(2) - 48x + 64`

• cancel equal terms

`- 32x = - 48x + 64`

• move the variable to the left

`- 32x = + 48x = 64`

• collect like terms

`16x = 64`

• divide both sides

`= \: \: x = 4`

• check the solution

`3 √(4) = (8)/( √(9 * 4 - 32) ) + √(9 * 4 - 32)`

• simplify

`6 = 6`

• so the solution is

`≈ \: \: x = 4`

`\huge \color {cyan}{ \tt{hope \: \: it \: \: helps}}`

Answer 2

Explanation:

`3√(x)=(8)/(√(9x-32))+√(9x -32)\\\\\\3√(x)=(8*√(9x-32))/((√(9x-32))*(√(9x-32)))+√(9x-32)\\\\3√(x)=(8*√(9x-32))/(9x-32)+√(9x-32)\\\\\\3√(x)=(√(9x-32))((8)/(9x-32)+1)\\\\(3√(x))/(√(9x-32))=(8+9x-32)/(9x-32)\\\\(3√(x))/(√(9x-32))=(9x - 24)/(9x-32)\\\\Take \ square\\\\((3√(x))/(√(9x-32)))^(2)=((9x-24)/(9x-32))^(2)\\\\(9x)/(9x-32)=((9x-24)^(2))/((9x-32)^(2))\\\\`

9x*(9x - 32) = (9x- 24)²

9x*9x - 9x*32 = 81x² - 2*9x*24 + 576

81x² - 288x = 81x² - 432x + 576

81x² - 288x - 81x² + 432x - 576 = 0

81x² - 81x² - 288x + 432x - 576 = 0

144x - 576 = 0

144x = 576

x = 576/144

x =4