If x+y=19 and xy=78, find y−x?

Zackary Diaz

Zackary Diaz

Answered question

2022-11-03

If x+y=19 and xy=78, find y−x?

Answer & Explanation

mangoslush27fig

mangoslush27fig

Beginner2022-11-04Added 15 answers

As x+y=19 and xy=78, we have
( x + y ) 2 = x 2 + 2 x y + y 2
i.e. 19 2 = x 2 + y 2 + 2 × 78
i.e. x 2 + y 2 = 19 2 - 2 × 78 = 361 - 156 = 205
Hence, ( y - x ) 2 = y 2 + x 2 - 2 x y = 205 - 2 × 78 = 205 - 156 = 49
and y - x = ± 7
In fact we can solve for x and y and the two numbers will be 13 and 6 or 6 and13.

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