CBSE Class 10 Answered
1. Prove that if x and y are both odd positive integers then x²+y² is even but not divisible by 4.
2. use Euclid's algorithm to find HCF of 1190 and 1445. Express the HCF in the form 1190m+1445n.
Asked by roysubarna2016 | 13 Jun, 2018, 06:53: PM
Expert Answer
Let the two odd positive numbers be x = 2k + 1 a nd y = 2p + 1
Hence x2 + y2 = (2k + 1)2 + (2p + 1)2
= 4k2 + 4k + 1 + 4p2 + 4p + 1
= 4k2 + 4p2 + 4k + 4p + 2
= 4(k2 + p2 + k + p) + 2
Clearly notice that the sum of square is even the number is not divisible by 4.
Hence if x and y are odd positive integers, then x2 + y2 is even but not divisible by 4
Hence x2 + y2 = (2k + 1)2 + (2p + 1)2
= 4k2 + 4k + 1 + 4p2 + 4p + 1
= 4k2 + 4p2 + 4k + 4p + 2
= 4(k2 + p2 + k + p) + 2
Clearly notice that the sum of square is even the number is not divisible by 4.
Hence if x and y are odd positive integers, then x2 + y2 is even but not divisible by 4
Answered by Arun | 14 Jun, 2018, 10:42: AM
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