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

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) (Show Source): You can put this solution on YOUR website!
Two numbers x and y, let .
----the first part of description

-
----the second part of description

Two formulas for sqrt(xy) must be equal.

AND .

This seems to make possible many solutions for x and y to form irrational and .

One example, but not the only example, should be and .
Their square roots are irrational.
I did NOT check these results.

Answer by MathTherapy(10552) (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:
Larger irrational number:
You can do the check!!
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