SOLUTION: the sum of two irrational numbers multiplied by the larger one is 70 and their difference is multiplied by the smaller one is 12

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Question 899344: the sum of two irrational numbers multiplied by the larger one is 70 and their difference is multiplied by the smaller one is 12
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39618) About Me  (Show Source):
You can put this solution on YOUR website!
Two numbers x and y, let x%3Cy.
%28sqrt%28x%29%2Bsqrt%28y%29%29sqrt%28y%29=70----the first part of description
sqrt%28xy%29%2By=70
sqrt%28xy%29=70-y
-
%28sqrt%28y%29-sqrt%28x%29%29sqrt%28x%29=12----the second part of description
sqrt%28xy%29-x=12
sqrt%28xy%29=x%2B12

Two formulas for sqrt(xy) must be equal.
70-y=x%2B12
highlight_green%28x%2By=58%29 AND highlight_green%28x%3Cy%29.

This seems to make possible many solutions for x and y to form irrational sqrt%28x%29 and sqrt%28y%29.

One example, but not the only example, should be highlight%28x=28%29 and highlight%28y=30%29.
Their square roots are irrational.
I did NOT check these results.

Answer by MathTherapy(10552) About Me  (Show Source):
You can put this solution on YOUR website!

the sum of two irrational numbers multiplied by the larger one is 70 and their difference is multiplied by the smaller one is 12


Smaller irrational number: highlight_green%28sqrt%288%29%29

Larger irrational number:  highlight_green%28sqrt%2850%29%29

You can do the check!! 



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