# Test 2 soru8

x, y ve z pozitif tam sayılardır

X×Y=22
Y×Z=26
Olduğna göre x+y+z toplamı kaçtır

@sorumatikbot

## karacakader said x, y ve z pozitif tam sayılardır, X×Y=22 ve Y×Z=26 olduğuna göre x+y+z toplamı kaçtır?

To solve this problem, we need to determine the values of ( x, y, ) and ( z ) such that ( x \times y = 22 ) and ( y \times z = 26 ) with ( x, y, ) and ( z ) being positive integers. Let’s follow these steps:

1. Analyze the Equations:

• Equation 1: ( x \times y = 22 )
• Equation 2: ( y \times z = 26 )
2. Prime Factorization:

• Factorize 22: ( 22 = 2 \times 11 )
• Factorize 26: ( 26 = 2 \times 13 )
3. Identify Possible Values for ( y ):

• ( y ) must be a common factor of both 22 and 26.
• The common factors are 1 and 2, considering ( y ) must be a common divisor of their prime factors.
4. Determine ( (x, y, z) ) for Each Possible ( y ):

• Case 1: ( y = 1 )

• If ( y = 1 ), then from ( x \times 1 = 22 ), we get ( x = 22 ).
• From ( 1 \times z = 26 ), we get ( z = 26 ).
• This solution yields ( x + y + z = 22 + 1 + 26 = 49 ).
• Case 2: ( y = 2 )

• If ( y = 2 ), then from ( x \times 2 = 22 ), we get ( x = 11 ).
• From ( 2 \times z = 26 ), we get ( z = 13 ).
• This solution yields ( x + y + z = 11 + 2 + 13 = 26 ).

Examining our cases, we see that ( y = 2 ) provides a consistent set of positive integers for ( x, y, ) and ( z ), whereas ( y = 1 ) does not satisfy the integer constraint for ( z ).