Question

the sum of three consequtive positive numbers is 50. Find the integers

Answer 1

Hey mate here is your answer:

Step-by-step explanation:

Let the first number be x

second be x + 1

third be x + 2

▪ The sum of squares is 50

x² + ( x + 1 )² + ( x + 2 )² = 50

x² + x² + 1 + 2x + x² + 4 + 4x = 50

3x² + 5 - 50 + 6x = 0

3x² - 45 + 6x = 0

x² - 15 + 2x = 0

x² + 2x - 15 = 0

x² + 5x - 3x - 15 = 0

x ( x + 5 ) - 3 ( x + 5 ) = 0

( x - 3 ) ( x + 5 ) = 0

* ( x - 3 ) = 0

x = 3

* ( x + 5 ) = 0

x = -5 ( neglected , because it is given that the integer are positive )

So,

First number x = 3

second number x + 1

= 4

Third number x + 2

= 5

So, the numbers are 3 , 4 and 5