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Simplify \(\frac{\sqrt{45 + \sqrt{1}} + \sqrt{45 + \sqrt{2}} + \sqrt{45 + \sqrt{3}} + \dots + \sqrt{45 + \sqrt{2024}}}{\sqrt{45 - \sqrt{1}} + \sqrt{45 - \sqrt{2}} + \sqrt{45 - \sqrt{3}} + \dots + \sqrt{45 - \sqrt{2024}}}\)

 Jan 27, 2019
 #1
avatar+701 
+1

Assuming that the numberator is the same as the denominator, the answer is \(\boxed{1}\)

 

Treat \(\sqrt{45 + \sqrt{1}} + \sqrt{45 + \sqrt{2}} ... + \sqrt{45 + \sqrt{2024}}\) as X. We will have \(\dfrac{X}{X}\), which simplifies into 1. 

 

Hope this helps, 

- PM

 Jan 27, 2019
 #2
avatar+101729 
0

PM it is not 1/1 

The top has + signs and the bottom has - signs. So the ansswer is more than 1

Melody  Jan 27, 2019

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