Question

HCF of 182 and 39 can be expressed as linear combination of X and y as 182 X + 39y .
find the value of x and y​

Answer 1

Answer

• The value of x = -1 and y = 5.

Given

• H.C.F. of 182 and 39 can be expressed as linear combination of x and y as 182x + 39y.

To Do

• To find the value of x and y.

Step By Step Explanation

• Step 1.
• First we need to find the HCF (182,39).

Using Euclid's algorithm :

Let's find the H.C.F.

$\longmapsto \sf182 = 39 \times 4 + 26 \\ \\ \longmapsto \sf39 = 26 \times 1 + 13 \\ \\ \longmapsto \sf 26 = \bold{13} \times 2 + 0 \\ \\ \longmapsto\underline{ \boxed{\pink{HCF = 13}}} \: \: \: \: \: \bigstar$

Hence H.C.F. = 13.

• Step 2.
• To find the value of x and y.

So let's do it !!

$\longmapsto \sf13 = 39 - 26 \\ \\ \longmapsto \sf13 = 39 - (182 - 39 \times 4) \\ \\\longmapsto \sf 13 = 39 - 182 + 39 \times 4 \\ \\\longmapsto \sf 13 = 39 \times 5 - 182 \\ \\ \longmapsto \bold{13 = 182x + 39y} \\ \\\longmapsto \sf 13 = - 182 + 39 \times 5 \\ \\ \longmapsto \sf13 = 182( - 1) + 39(5) \\ \\\longmapsto \sf \underline{\boxed{ \bold{ \green{ x = - 1}}}} \: \: and \: \: \underline{ \boxed{ \bold{ \red{ y = 5}}}} \: \: \: \: \: \bigstar$

Therefore, the value of x = -1 and y = 5.

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Answer 2

Step-by-step explanation:

x=1 y=5. this is your answer. correct