Suma a 3 numere naturale este 163. scazand al treilea numar din suma primelor doua numere, obtinem 67. scazand primul numar din suma ultimelor 2 numere, obtinem 37. determinati cele 3 numere

x=63, y=52, z=48

Step-by-step explanation:

The complete question in english is:

The sum of 3 natural numbers is 163. By subtracting the third number from the sum of the first two numbers, we get 67. By subtracting the first number from the sum of the last 2 numbers, we get 37. Determine the 3 numbers

According to this we have a system with three equations and three unknown values:

(1)

(2)

(3)

Let's begin by isolating from (1):

(4)

And substitute (4) in (2):

(5)

Isolating :

(6) We have found the first number

Substituting (6) in (1):

(7)

Adding (7) to (3):

We have the following:

Isolating :

(8) This is the second number

Substituting (6) and (8) in (1):

(9)

Isolating :

(10) This is the third number

64

Step-by-step explanation:

Given

we need to find a number that makes perfect square

We apply completing the square method

In completing the square method, take the coefficient of x  , divide it by 2  and then square it

coefficient of x  is 16

16 divide by 2 is 8

So 64 will be added to the given expression to make perfect square trinomial .