Examples of Math Problems: is it possible to write two real numbers whose sum is 4 and whose product is 5?

Thursday, May 9, 2013

is it possible to write two real numbers whose sum is 4 and whose product is 5?

Your Answer:

y=5%2Fx

%0D%0Ax%2B5%2Fx=5%0D%0A

%0D%0Ax%5E2%2B5=5x%0D%0A

%0D%0Ax%5E2-5x%2B5=0%0D%0A

this is clearly irreducible...so let's use the quadratic formula...

x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+

x+=+%28-%28-5%29+%2B-+sqrt%28+%28-5%29%5E2-4%2A1%2A5+%29%29%2F%282%2A1%29+

x+=+%285+%2B-+sqrt%28+5+%29%29%2F2+

So, yes if we extend our search out to all real numbers we can find two irrational numbers that meet our requirements

:)

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