x, y ve z pozitif tam sayılardır
X×Y=22
Y×Z=26
Olduğna göre x+y+z toplamı kaçtır
karacakader said x, y ve z pozitif tam sayılardır, X×Y=22 ve Y×Z=26 olduğuna göre x+y+z toplamı kaçtır?
Answer:
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:
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Analyze the Equations:
- Equation 1: ( x \times y = 22 )
- Equation 2: ( y \times z = 26 )
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Prime Factorization:
- Factorize 22: ( 22 = 2 \times 11 )
- Factorize 26: ( 26 = 2 \times 13 )
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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.
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Determine ( (x, y, z) ) for Each Possible ( y ):
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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 ).
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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 ).
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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 ).
Final Answer:
Therefore, the sum ( x + y + z ) is ( \boxed{26} ).