simple algebra

Algebra Level 2

Evaluate

45 − 2000 + 45 + 2000 \sqrt{45-\sqrt{2000}}+\sqrt{45+\sqrt{2000}} .

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The answer is 10.

Victor Loh by Victor Loh , 19, Singapore

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1 solution

x 2 + y 2 = 90 x y = 5 ⟹ ( x + y ) 2 = 100 ⟹ x + y = 10 { x }^{ 2 }+{ y }^{ 2 }=90\\ xy=5\\ \Longrightarrow (x+y{ ) }^{ 2 }=100\\ \Longrightarrow x+y=10

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Very clever. How about this for a simpler approach.

Square the original expression to make the surds cancel and leave you with 100. Then square root to get the 10!

Abigail Kent - 3 years, 8 months ago

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