1. The product of two consecutive integers is
56. Find the integers.
Answers
Answered by
4
Step-by-step explanation:
7 × 8 = 56
Then the second number is
n
+
1
The product is
n
×
(
n
+
1
)
=
56
⇒
n
2
+
n
−
56
=
0
Known:
7
×
8
=
56
. However the equation's 56 is nagetive, so one of the 7 and 8 is negative.
The equation has
+
n
so the larger of the two is positive. Giving:
(
n
−
7
)
(
n
+
8
)
=
0
⇒
n
=
+
7
and
n
=
−
8
As a first number
n
=
−
8
is not logical so the first number is
n
=
7
Thus the second number is 8.
Answered by
2
Answer:
The two consecutive integers are x and x+1
(x)(x + 1) = 56
x^2 + x = 56
x^2 + x - 56 = 0
x^2 + 8x - 7x - 56 = 0
x(x + 8) -7(x + 8) = 0
(x - 7)(x + 8) = 0
x = 7 or -8
If x = 7 ==> x + 1 = 7 + 1 = 8
If x = -8 ==> x + 1 = -8 + 1 = -7
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