Question

Rút gọn biểu thức sau
(2/2-√5 - 2/2+√5):√20

Answer 1

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let's solve for value of (2/2-√5 - 2/2+√5) :

• 
  `(2)/(2 - √(5) ) - (2)/(2 + √(5) )`
• 
  `\frac{2(2 + √(5) ) - 2(2 - √(5) )}{ {2}^(2) - 5}`
• 
  `(4 + 2 √(5) - 4 + 2 √(5) )/(4 - 5)`
• 
  `(4 √(5) )/( - 1)`
• 
  `- 4 √(5)`

now, let's simply the ratio :

• 
  `- 4 √(5) : √(20)`
• 
  `( - 4 √(5) )/( √(20) )`
• 
  `( - 4)/( √(4) )`
• 
  `- √(4)`

Therfore , the required ratio is :

• 
  `- √(4) :1`