X and y are two numbers which when divided by 6 leaves a remainder of 4 and 5 respectively
Answers
Answer:
A.T.Q
X/6=4
X=4*6
X=24
Y/6=5
Y=5*6
Y=30
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.