Question

The difference of two positive numbers is 7 and the sum of their squares is 109. Find the numbers.

Answer 1

Answer:

$Numbers\ are\ 58\ and\ 51.$

Step-by-step explanation:

The the numbers are $x\ and\ y$.

Difference:

$Difference\ of\ numbers=7\\\\x-y=7....................eq(1)$

Sum:

$Sum\ of\ numbers=109\\\\x+y=109...........................eq(2)$

Solve $eq(1)$ and $eq(2)$.

$eq(1)+eq(2)\\\\x-y+x+y=7+109\\\\2x=116\\\\x=58\\\\Now\ from\ equation\ 1\\\\x-y=7\\\\y=x-7\\\\y=58-7\\\\y=51$