Show that hcf of 420 and 130 Can be
expressed as a linear Combination of 420
and 130. also show that this representation
is mot unique
Answers
Answer:
We'll follow the Euclid Algorithm to solve this problem,
420 = 3*130 + 30.......(1)
Now,
130 = 4*30 + 10 ........(2)
30 = 3*10+0.....(3)
Hence the HCF of both these numbers will be 10.
From equation 2 :
HCF (420,130) = 10 = (130-4*30)
and, 30 = 420-(3*130)
So,
10 = (130-4*(420-3*130)) = 13*130 + (-4)*420......(4)
And hence we've shown that the GCD can be shown as a linear combination
To prove that it's not unique
Let's add and subtract the number
(420)*(130)*m
to equation 4
We get
10 = 13*130 + (-4)*420 + (420m)*130 - (130m)*420
=(13+420m)*130 + (-4-130m)*420
So, we can clearly see that on putting in different values of m as an integers we can get different ways of expressing the HCF as a linear combination of both the number.
I really hope this solution was clear and i hope this helps you !
Answer:
X=3 AND Y =1
Step-by-step explanation:
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