the product of two consective odd integers is sixty-three. find all such number.
Hint:
What is the square root of 63?
What are the factors of 63?
3^2(7)
To find the consecutive odd integers whose product is 63, follow these steps:
Step 1: Let's assume the first odd integer as x.
Step 2: The next consecutive odd integer will be x + 2 since consecutive odd integers have a difference of 2.
Step 3: Now, we can set up an equation based on the given information. The product of these two odd integers is 63, so:
x * (x + 2) = 63
Step 4: Expand the equation:
x^2 + 2x = 63
Step 5: Rearrange the equation to bring it to standard quadratic form:
x^2 + 2x - 63 = 0
Step 6: To factorize the quadratic equation, find two numbers that multiply to give -63, but add up to 2. The numbers are 7 and -9:
(x + 9)(x - 7) = 0
Step 7: Set each factor equal to zero and solve for x:
x + 9 = 0 --> x = -9
x - 7 = 0 --> x = 7
Step 8: So, the two consecutive odd integers whose product is 63 are -9 and 7.
Therefore, the numbers -9 and 7 are the consecutive odd integers whose product is 63.