Math, asked by annika9139, 1 year ago

X and y are two numbers which when divided by 6 leaves a remainder of 4 and 5 respectively

Answers

Answered by kraj78901
9

Answer:

      A.T.Q

X/6=4

X=4*6

X=24

Y/6=5

Y=5*6

Y=30

Answered by franktheruler
19

Question:

Two numbers, x and y, when divided by 6 leave a remainder of 4 and 5, what will be the remainder when x² +y² is divisible by 6?

Answer:

According to the question, when x is divided by 6 then a remainder of 4 is obtained.

So, x = 6a + 4

Similarly y = 6b + 5 [ where a and b are two positive integers. ]

Squaring the both side of equations:

X² = 36a² + 48a + 16    ………………….(i)

Y² = 36b² + 60b + 25……………………..(2)

 

Now add equation (i) and equation (ii)

X² + Y² = 36a² + 36b² + 48a + 60b + 41

X² + Y² = 6 ( 6a² + 6b² + 8a + 10b + 6) + 5

So

X² + Y² = 6m + 5 [ where m = (6a² + 6b² + 8a + 10b + 6)  ]

Now by euclids division lemma X²+Y² when divided by 6 leaves a remainder 5.

So the answer is 5.

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