Question

if d is HCF of 40 and 65,find the value of x and y to satisfy d=40x+65y

Answer 1

Given integers,
40 and 65
Applying Euclid's division lemma we get,
65=40×1+25......................................1
Applying Euclid's division lemma to 40 and 25 we get,
40=25×1+15......................................2
Applying Euclid's division lemma to 25 and 15 we get,
25=15×1+10........................................3
Applying Euclid's division lemma to 15 and 10 we get,
15=10×1+5..........................................4
Applying Euclid's division lemma to 10 and 5 we get,
10=5×2+0...........................................5
eq1,eq2,eq3,eq4 can also be written as,
65-40×1=25..................................…..6

40-25×1=15........................................7

25-15×1=10.........................................8

15-10×1=5............................................9
Eq9 we have,
5=15-10×1
By putting eq8 in above eq we get,
5=15-(25-15×1)1

5=15-25×1+15×1

5=15×2-25×1
By putting eq7 in above eq we get,
5=(40-25×1)2-25×1

5=40×2-25×2-25×1

5=40×2-25×3
By putting eq6 in above eq we get,
5=40×2-(65-40×1)3

5=40×2-65×3+40×3

5=40×5-65×3

5=40(5)+65(-3)
Given equation,
d=40x+65y
Here d is HCF.
Therefore , 5=40x+65y
On comparing we get,
x=5 and y=-3
Hence value of x=5 and value of y=-3

Answer 2

Answer:

Step-by-step explanation:

d9e2bf953ae88c2ac886399c9f49f34b.pdf