Solve the system. x + y - z = 17 y +z = 1 z = -3
2 answers:
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The equation in terms of x is x(x + 2) = 99 or
The pairs of integers are -11 and -9 or 9 and 11
<em><u>Solution:</u></em>
Let the two consecutive odd integers be x and x + 2
Let "x" be the smallest integer
Given that product of two consecutive odd integers is 99
To find: an equation in terms of x
Product of x and x + 2 = 99
Thus the equation in terms of x is found
Let us solve the above equation to find all pairs of integers
Solve the quadratic equation by grouping method
Middle term 2x can be written as 11x - 9x
Now group the terms,
Take "x" as common term from first group and 9 as common term from second group
Now take x + 11 as common term,
Equating to zero we get,
x + 11 = 0 or x - 9 = 0
x = -11 or x = 9
<em><u>When x = -11 :</u></em>
x + 2 = -11 + 2 = -9
Thus first set of two consecutive odd integers are -11 and -9
<em><u>When x = 9 :</u></em>
x + 2 = 9 + 2 = 11
Thus second set of two consecutive odd integers are 9 and 11
