Using euclid''s algorithm find the value of x & y, Mathematics

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If d is the HCF of 30, 72, find the value of x & y satisfying d = 30x + 72y.

(Ans:5, -2 (Not unique)

Ans: Using Euclid's algorithm, the HCF (30, 72)

72 = 30 × 2 + 12

30 = 12 × 2 + 6

12 = 6 × 2 + 0

HCF (30,72) = 6

6=30-12×2

6=30-(72-30×2)2

6=30-2×72+30×4

6=30×5+72×-2

∴ x = 5, y = -2

Also 6 = 30 × 5 + 72 (-2) + 30 × 72 - 30 × 72

Solve it, to get

x = 77, y = -32

Hence, x and y are not unique

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