Prove that if x & y are odd positive integers then x^2+y^2 is even but not divisible by 4
Sneha Manoharan , 11 Years ago
Grade 10
10 grade maths> Prove that if x & y are odd positive inte...
1 Answers
S. Haris Ahmed Irfan
all odd positive integers are of form 2q+1
therefore let x=2q+1 and y=2p+1 (where p and q are integers)
x^2=(2q+1)^2=4q^2+1+4q
y^2=(2p+1)^2=4p^2+1+4p
therefore x^2+y^2=4q^2+1+4q+4q^2+1+4q
after rearranging
4(q^2+p^2+p+q)+2
this number is clearly even but is not divisible by 4 {since 2 is added at the end}
LIVE ONLINE CLASSES
Prepraring for the competition made easy just by live online class.
Full Live Access
Study Material
Live Doubts Solving
Daily Class Assignments
Other Related Questions on 10 grade maths
How do you find the Maclaurin series for tanx?
How do you find the Maclaurin series for tanx?
10 grade maths
1 Answer Available
Last Activity: 7 Months ago
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the equation is not about the fifth postulate.)
Why is Axiom 5, in the list of Euclid’s axioms, considered a ‘universal truth’? (Note that the equation is not about the fifth postulate.)
10 grade maths
1 Answer Available
Last Activity: 7 Months ago
The smallest composite number is ______.
(a) 2
(b) 4
(c) 1
(d) None of these
The smallest composite number is ______.
(a) 2
(b) 4
(c) 1
(d) None of these
10 grade maths
1 Answer Available
Last Activity: 7 Months ago
Find the arithmetic mean of the first ten odd natural numbers.
Find the arithmetic mean of the first ten odd natural numbers.
10 grade maths
1 Answer Available
Last Activity: 7 Months ago