Question

plz solve this question

Answer 1

apply Euclid's division algorithm for finding HCF
$45 = 27 \times 1 + 18 \\ 27= 18 \times 1 + 9 \\ 18= 9 \times 2 + 0$
so HCF is 9.
to write in the form ,as given in the question,starts from second last equation
$9 = 27 - 18 \times 1 \\ 9 = 27 - 18 \\ 9 = 27 - (45 - 27) \: \: \: \: from \: eq \: 1\\ 9 = 27 - 45 + 27 \\ 9 = 2 \times 27 + ( - 1) \times 45 \\ 9 = x27 + y45 \\ so \: x = 2 \\ y = - 1$