CBSE Class 10 Answered
If "d" is the HCF of 56 and 72 . find x and y . satisfying d= 56x+72y
Asked by arindeep.singh | 21st Apr, 2020, 06:50: PM
Expert Answer:
Here, 56 < 72
Applyig Euclid's Divisio Lemma,
72 = 56 × 1 + 16 (r ≠ 0) ... (i)
56 = 16 × 3 + 8 (r ≠ 0) ... (ii)
16 = 8 × 2 + 0
Since, r = 0
→HCF(56, 72) = 8 = d
8 = 56 - 16 × 3 .... from (ii)
= 56 - [72 - (56 × 1)] × 3 ... from (i)
= 56 × 4 + 72 × (-3)
= 56 × x + 72 × y
→ x = 4 and y = -3
Q) In this question how 56* 4 + 72 * (-3) has come in the last 2nd step.
Asked by arindeep.singh | 23 Apr, 2020, 05:55: PM
Expert Answer
8 = 56 - 16 × 3 .... from (ii)
= 56 - [72 - (56 × 1)] × 3 ... from (i)
= 56 - 72× 3 + (56 × 1)× 3
= 56 × 4 - 72× 3
= 56 × 4 + 72 × (-3)
= 56 × x + 72 × y
Answered by Arun | 23 Apr, 2020, 07:03: PM
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