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Answer:
The smaller number is 4√2 and the larger number is (4√2 + 1).
Step-by-step explanation:
Let the two numbers be <em>x </em>and <em>y</em>, where <em>y</em> is the larger of the two numbers.
Since <em>y</em> is the larger number, it is one more than the smaller number. So:
When negative two times the smaller is added to the square of the larger, the result is 33. In other words:
Substitute:
Solve for <em>x</em>. Square:
Simplify:
Subtract one from both sides:
And take the square root of both sides:
Since <em>y</em> is positive, we can ignore the negative case. So, the smaller number is:
And the larger number is: