SOLUTION: The larger of two numbers is one less than twice the smaller number. The difference of thier squares is 33 . Find the numbers.

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Question 169638: The larger of two numbers is one less than twice the smaller number. The difference of thier squares is 33 . Find the numbers.
Answer by jojo14344(1512) About Me  (Show Source):
You can put this solution on YOUR website!
Larger number=2x-1
Smaller number=x
Condition: The difference of the squares is 33:
%282x-1%29%5E2-x%5E2=33 -----------> EQN 1
4x%5E2-4x%2B1-x%5E2=33
3x%5E2-4x%2B1-33=0
3x%5E2-4x-32=0, solve via Quadratic Eqn: x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
where-------->system%28a=3%2Cb=-4%2Cc=-32%29
Continue and you get 2 values ---> system%28highlight%28x=4%29%2Chighlight%28x=-8%2F3%29%29
Therefore, x=4=smaller & 2%2A4-1=8-1=7=Larger, Answer
.
Check via EQn 1:
7%5E2-4%5E2=33
49-16=33
33=33
Thank you,
Jojo