Question

The product of two positive consecutive integers is equal to 56. Find the two integers. The sum of the squares of two consecutive numbers is equal to 45. Find the two numbers

Answer 1

Let the two integers be x and x+2.
Now,
x + x + 1 = 56
2x + 1     = 56
 2x          = 55
 x            = 27.5
and x+1 = 28.5

Hence,the numbers are 27.5 and 28.5.

Answer 2

Define x:

Let one of the number be x

And the other be (x + 1)

Solve x:

x ( x + 1) = 56

x² + x  = 56

x² + x - 56 = 0

(x - 7) (x + 8)= 0

x = 7 or x = - 8 (rejected, since it is not positive)

Find the numbers:

One number = x = 7

The other number = x + 1 = 7 + 1 = 8

Answer: The numbers are 7 and 8

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* There is a mistake in the question. The sum of the squares of the 2 numbers is 145 and not 45.

Define x:

Let one of the number be x

And the other be (x + 1)

Solve x:

The sum of the squares of the 2 numbers is 145

x² + (x + 1)² = 145

x² + x² + 1 + 2x = 145

2x² + 2x - 144 = 0

x² + x - 72 = 0

(x - 8) (x + 9) = 0

x = 8 or x = -9 (rejected, since it cannot be negative)

Find the numbers:

one number = x = 8

The other number = x + 1 = 8 + 1 = 9

Answer: The numbers are 8 and 9