Question

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The question is below.


`2 √(x) - 14 = (288)/( √(x) )`
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Answer 1

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`refer \: to \: the \: above \: attatchment`

Answer 2

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Here's the solution ~

• 
  `\sf 2√(x) - 14 = (288)/( √(x) )`

• 
  `\sf √(x) (2 √(x) - 14) = 288`

• 
  `\sf 2x - 14 √(x) - 288 = 0`

• 
  `\sf2x - 32 √(x) + 18 √(x) - 288 = 0`

• 
  `\sf2 √(x) ( √(x) - 16) + 18( √(x ) - 16 ) = 0`

• 
  `\sf(2 √(x) + 18) ( √(x) - 16) = 0`

There are two cases now ~

Case #1

• 
  `\sf2 √(x) + 18 = 0`

• 
  `\sf2 √(x) = - 18`

• 
  `\sf √(x) = - 18 / 2`

• 
  `\sf √(x) = - 9`

• 
  `\sf x = ( - 9) {}^(2)`

• 
  `\sf{x = 81}`

Case #2

• 
  `\sf √(x) - 16 = 0`

• 
  `\sf √(x) = 16`

• 
  `\sf x = (16) {}^(2)`

• 
  `\sf{x = 256}`