one positive number is 3 bigger than another number. when the larger number is added to the square of the smaller one, the result is 33

Question

what would the equation be

Answer 1

We can represent the first positive number as a and the second as b.

"one positive number is 3 bigger than another number" tells us that a = b + 3.

"when the larger number is added to the square of the smaller one" a is the larger number and the square of the smaller is b^2.

"the result is 33"

means a + b² = 33.

 

Since we know a = b+3. we can rewrite the equation as b+3+b²=33. Subtract 33 from both sides.

b² + b - 30 = 0

 

since I know that -5*6 is -30 and -5 + 6 = +1(the coefficient of the middle term), I know to use these values to factor the quadratic equation.

Now we have (b-5)(b+6) = 0, so b = 5, or -6, and since a = b+3, a = 8, or -3. Since a is positive, we know the latter is not possible, so a = 8, and b = 5.

This matches that a+b² = 33 because 8 + 5² = 8+25 = 33.