→ D is the HCF of 1155 and 506. Find x and y satisfying D = 1155x + 506y also show x and y are not unique.
Answers
Step-by-step explanation:
Refer to the attachment...
Therefore x = 0 and y = 66 are the values that can satisfy the given equation and they can't be unique in any case.
Given:
The numbers given are 1155 and 506.
Equation given is D = 1155x + 506y.
Where D is the HCF of the given numbers.
To Find:
The values of 'x' and 'y'.
Solution:
The given question can be easily solved as shown below.
Given numbers are 1155 and 506.
Prime Factors of 1155 = 3 × 5 ×7 × 11
Prime Factors of 506 = 2 × 11 × 23
HCF of two numbers is the multiplication of common prime factors of both numbers.
Here 11 is the common prime factor of 1155 and 506.
So HCF of 1155 and 506 is 11.
Then the equation becomes 11 = 1155x + 506y
⇒ 11 = 11 [ ( 3 × 5 ×7 )x + ( 2 × 23 )y ]
⇒ 1 = 105x + 66y
Definitely 'x' cannot be equal to 'y'.
If x = 0 ⇒ 1 = ( 105 × 0 ) + ( 66y )
⇒ 1 = 0 + 66y
⇒ y = 1/66
Therefore x = 0 and y = 66 are the values that can satisfy the given equation and they can't be unique in any case.
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