17. Write a quadratic equation to find two consecutive odd natural numbers whose product is 63. Then find the numbers

7 and 9

Step-by-step explanation:

So we want two consecutive odd numbers whose product is 63.

Let's write an equation.

Let's let n be a random integer: doesn't matter what it is. Therefore, the first integer must be 2n+1.

This is because we're letting n be whatever it wants to be. If we multiply that whatever number by 2, then it will turn even. If we add 1 to an even number, it becomes odd.

Therefore, our first odd number is (2n+1). Our second, then, must be (2n+3).

Multiply them together. They equal 63. Thus:

Expand:

Combine like terms:

Subtract 63 from both sides:

Divide both sides by 4:

And now, factor:

Zero Product Property:

Find n:

So, we've found n.

Then the first integer is either:

Evaluate:

However, we want two consecutive odd natural numbers. So, ignore the -9.

Therefore, our first odd integer is 7.

And our second one would be 9.

So, our answer is 7 and 9.

And we're done!

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step-by-step explanation:

because i said it is