A positive real number is 1 more than another. When -2 times the smaller is added to the square of the larger, the result is 33. Find the numbers.

The smaller number is 4√2 and the larger number is (4√2 + 1).

Step-by-step explanation:

Let the two numbers be x and y, where y is the larger of the two numbers.

Since y 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 x. Square:

Simplify:

Subtract one from both sides:

And take the square root of both sides:

Since y is positive, we can ignore the negative case. So, the smaller number is:

And the larger number is:

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step-by-step explanation:

2

step-by-step explanation: