Question

if D is the HCF of 56 and 72 find X and Y satisfying d = 56 X + 72 Y show that x and y are not unique???

Answer 1

see, the abvove attachment.......

CHEERS☺

Answer 2

THIS QUESTION IS FROM THE BOOK MATHEMATICS RD SHARMA CLASS 10 :

BY APPLYING EUCLID's DIVISION LEMMA TO 56 AND 72 :
72 = 56 × 1 +16 ------------ (1)
56 = 16 × 3 + 8 ------------ (2)
16 = 8 × 2 + 0 -------------- (3)

THEREFORE HCF OF 56 AND 72 = 8
FROM (2) -- 8 = 56 - 16 ×3
8 = 56 - (72-56×1) ×3 (from 1)
8 = 56 - 3 × 72 + 56 × 3
8 = 56 × 4 + (-3) × 72
therefore , x = 4 and y = -3

Now, 8 = 56 × 4 + (-3) × 72
8 = 56 × 4 + (-3) × 72 - 56 × 72 + 56 × 72
8 = 56 × 4 -56 × 72 + (-3) × 72 + 56 ×72
8 = 56 × (4-72) + {(-3) + 56} × 72
8 = 56 × (-68) + (53) × 72

therefore x = -68 and y = 53


HENCE , x and y are not unique.........