Math, asked by jyotiramsalunke8701, 1 year ago

Use elucids algorithm to find the hcf of85 and 51 and express them in the form of 85x+51y where x and y are integers

Answers

Answered by kabikabbu7899pa4ozh
0
According to Euclid's division lemma 
a=bq+r, 0<=r<b
85=51*1+34
51=34*1+17
34=17*2+0

17=[51-34*1]
17=[51-{85-(51*1)}*1]
17=[51-85*1+51*1]
17=[51*2-85*1]
17=[(-85*1)+51*2]
17=85x+51y

x = (-1), y = 2

kabikabbu7899pa4ozh: if it is helpful plzz mark it as brainlist
Answered by YASH3100
3
HEYA!!!


HERE IS YOUR ANSWER,


=> HCF OF (85, 51)

=> 85 = 51×1 + 34 ---(i)

=> 51 = 34×1 + 17 ---(ii)

=> 34 = 17×2 + 0 ---(iii)

∵ HCF OF (85, 51) = 17

=> 17 = 51 - 34×1 [Using (ii)]

=> 17 = 51 - (85 - 51×1)×1 [Using (i)]

=> 17 = 51 - 85 + 51

=> 17 = 2×51 - 85

NOW,

=> On comparing with 85x + 51y, we get x = -1 and y = 2.


HOPE IT HELPS YOU,
THANK YOU.☺️☺️
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