Question

$\huge\mathfrak\purple{Hello\:Mate}$❤
Find the linear combination of :
(i)963 and 657
(ii)506 and 1155​

Answer 1

we need to find the HCF of 963 and 657 and express it as a linear combination of 963 and 657 by using Euclids division lemma,

963 = 657 x1 + 306

657= 306x2 + 45

306 =45 x 6 + 36

36 = 9x4 + 0

Hence HCF = 9

Now 9 = 45 - 36x1

= 45 - [306 -45 x6] x1

= 45 - [ 306 x 1 + 45x 6]

=45x 7 - 306 x1

=[ 657- 306 x2]x7 - 306x1

= 657x7 - 306x14 - 306x1

= 657 x7 - [963 - 657x1]x15

= 657 x7 - 963 x15 + 657 x15

= 657 x22 - 963 x 15

Hence obtained

second question : BYusing Euclis division lemma

a = bq + r ( 0lessthan or equal r less thsn b)

1155 = 506x2+ 143

506 = 143x3 + 77

143 = 77x1+ 66

66 = 11x6 +0

Therefore HCF = 11

Linear form:

506a + 1155b = 11

there are many solutions one of them

a= 16 and b = - 7

solution : 11 = 506 (16) + 1155( -7)

Hope this solution help you mark as brainliest answer

Answer 2

Step-by-step explanation:

HelloMate

refer the attachment