The product of two consecutive even integers is 168. Assuming the smaller integer to be X frame and equation for the statement .
Answers
Step-by-step explanation:
Consecutive even integers differ by 2. So if x is the smaller one, then x+2 is the bigger one and your equation is x(x+2) = 168, which can be rewritten as x^2+2x-168=0 and whose solutions can be found by means of the quadratic formula to be -14 and 12.
Answer:
Assuming smaller integer as x.
The larger integer = x + 2
(since they are consecutive even integers so, difference between them is 2.)
Thus, according to question, equation framed:
x (x+2) = 168
=> x² + 2x - 168 = 0
=> x² + 14x - 12x -168 = 0
=> x (x+14) -12(x+14) = 0
=> (x+14) (x-12) = 0
(for product of two real numbers equal to 0, at least one of them must be 0)
=> x + 14 = 0 or x-12=0
=> x = -14 or x = 12
therefore, x + 2 = -14 + 2 = -12
or x + 2 = 12 + 2 = 14.
Thus, we have two solutions for both the even integers.
smaller integer = -14 or 12
larger integer = -12 or 14
I hope it helped you!