1.

The product of two consecutive positive integers is 11 less than 11 times their sum. What are the two numbers?​

Answer»

Step-by-step explanation:

If the integers are

m

and

m

+

1

, then we are given:

m

×

(

m

+

1

)

=

m

+

(

m

+

1

)

+

11

That is:

m

2

+

m

=

2

m

+

12

SUBTRACT

2

m

+

12

from both sides to get:

0

=

m

2

−

m

−

12

=

(

m

−

4

)

(

m

+

3

)

This equation has solutions

m

=

−

3

and

m

=

4

We were told that

m

and

m

+

1

are positive, so we can reject

m

=

−

3

, LEAVING the unique solution

m

=

4

.

So the integers are

m

=

4

and

m

+

1

=

5

.


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