Question

If hcf of 210 and 55 can be expressible in form of 210x+55y find x and y

Answer 1

Answer:

x = -5 and y = 19

Step-by-step explanation:

here given 2 no.

first find HCF of 210 and 55

210 = 55 × 3 + 45

55 = 45 × 1 + 10

45 = 10 × 4 + 5

10 = 5 × 2 + 0

here HCF = 5

now we can write it as

5 = 45 - 10 × 4       = equation 1

10 = 55 - 45 × 1        = eq.2

45 = 210 - 55 × 3        = eq.3

now in equation 1 substitute values of 45 and 10 from eq 2 and 3

5 = 210 - 55 × 3 - ( 55 - 45 × 1 ) × 4

here again substitute the value of 45 by eq

now 5 = 210 - 55 × 3 - 55 × 4 - ( 210 - 55 × 3) × 4

5 = 210 - 55 × 7 ( add same no. multiplicands ) - 210 × 4 - 55 × 12

now same number side

5 = 55 × 19 + 210 × (-5)

so value of x = -5 and y = 19