Question

solve this question with full explanation I have read the question four five times but I didn't understand it please please please help me
I WILL MARK THE BEST AS BRAINLIEST...
QUESTION::
@@find HCF of 81 and 237 and Express it as linear combination of 81 and 237 that is HCF (81,237) = 81x + 237 y for some x and y ???​

Answer 1

Answer:

-38,13

Step-by-step explanation:

Given numbers are 81 and 237.

Among 81 and 237; 237 > 81.

Apply the euclid's division lemma, we get

231 = 81 * 2 + 75

Since remainder ≠ 0, we apply the division lemma to 81 and 75, we get

81 = 75 * 1 + 6

Since remainder ≠ 0, we apply the division lemma to 75 and 6, we get

75 = 6 * 12 + 3

Since remainder ≠ 0, we apply the division lemma to 6 and 3, we get

6 = 3 * 2 + 0

Here, the remainder is 0. Thus the divisor is 3

Therefore, HCF of 81 and 237 is 3.

Linear Combination:

3 = 75 - (85 - 75 * 1) * 12

  = 75 - (81 * 12 - 75 * 12)

  = 75 * 13 - 81 * 12

  = (237 - 81 * 2) * 13 - 81 * 12

  = (237 * 13 - 81 * 26) - 81 * 12

  = 237 * 13 - 81 * 38

  = 237 * 13 + 81 * (-38)

HCF(81,237) = 81x + 237y

                    = 81(-38) + 237(13)

Therefore, the values of x and y are -38 and 13.

Hope it helps!

Answer 2

3 = 75 - 6 x 12 => 3 = 75 - (81 - 75 x 1) x 12...............(1) Now, apply multiplication and distribution rule i.e. a(b+c)=ab+bc ? (1) becomes => 3 = 75 - (81 x 12 - 75 x 12) Now open the bracket...so sign changes from -75 to +75 => 3 = 75 - 81 x 12 + 75 x 12 => 3 = 75 + 75 x 12 - 81 x 12 => 3 = 75 (1 + 12) - 81 x 12 => 3 = 75 x 13 - 81 x 12...............(2) 75 = 237 – 81 x 2 ? from your step 1..............(3) Substitue (3) in (2) => 3 = (237 - 81 x 2) x 13 - 81 x 12 Apply again multiplication and distribution rule, => 3 = 237 x 13 - 81 x 2 x 13 - 81 x 12 => 3 = 237 x 13 - 81 x 26 - 81 x 12 => 3 = 237 x 13 - 81 (26 + 12) => 3 = 237 x 13 - 81 x 38....................(4) HCF(237,81) = 3 = 237 x 13 + 81 x (-38)