The product of two consecutive odd integers is 35. Find the integers
x(x+2)= 35
x^2 + 2x - 35 = 0
(x - 5)(x - 7) = 0
x = 5, 7
I WAS LOOKING FOR ,AN ANSWER
To find the two consecutive odd integers, we can solve the problem algebraically. Let's assume that the first odd integer is represented by 'x'. Since the next consecutive odd integer will be two units greater, it can be represented as 'x + 2'.
According to the problem, the product of these two integers is 35, so we can set up the equation:
x * (x + 2) = 35
Expanding the equation:
x^2 + 2x = 35
Rearranging the equation into quadratic form:
x^2 + 2x - 35 = 0
Now, we can solve this quadratic equation using factoring, completing the square, or the quadratic formula. In this case, we can factor the quadratic equation:
(x + 7)(x - 5) = 0
Setting each factor equal to zero and solving for 'x':
x + 7 = 0 or x - 5 = 0
If x + 7 = 0, then x = -7
If x - 5 = 0, then x = 5
Therefore, the two consecutive odd integers that have a product of 35 are -7 and -5, or 5 and 7.
find two consecutive odd integers whose product is 35
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