perplexus.info :: Just Math : Given Radical Real Product, Find the Square of Sum

Given Radical Real Product, Find the Square of Sum (Posted on 2023-05-25)

Each of x and y is a real number that satisfy this equation:

• {x+√(1+x²)}{y+√(1+y²)}= 1

Determine the value of (x+y)²

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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An obvious solution is (0,0), making (x+y)^2 = 0

On inspection, I see that (x,-x) is also a solution, so again (x+y)^2 = 0

Posted by Steve Herman on 2023-05-25 09:30:22

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