Question 934780

Please help me solve this problem:
two numbers have a different of 3.the sum of their square is 89.find the number
<pre><font face = "Tohoma" size = 4 color = "indigo"><b>Let the larger number be L
Then smaller = L - 3
Being that their squares sum to 89, we get: {{{L^2 + (L - 3)^2 = 89}}}
{{{L^2 + L^2 - 6L + 9 = 89}}}
{{{L^2 + L^2 - 6L + 9 - 89 = 0}}}
{{{2L^2 - 6L - 80 = 0}}}
{{{2(L^2 - 3L - 40) = 2(0)}}}
{{{L^2 - 3L - 40 = 0}}}
(L - 8)(L + 5) = 0
L, or larger number = 8       OR      - 5

If larger number = 8, then smaller number = 8 - 3, or 5
If larger number = - 5, then smaller number = - 5 - 3, or - 8

Numbers: {{{highlight_green(highlight_green(system(8_and_5_or,- 5_and_- 8))))}}}
You can do the check!! 
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