Property 10 For any natural number m greater than `1 (2m, m^2 - 1, m^2 + 1)` is a pythagorean triplet .

For every natural number m, (2m -1, 2m^2-2m, 2m^2–2m + 1) is a pythagorean triplet. True or false

If a and b are natural numbers and a gt b, then show that (a^(2) + b^(2)), (a^(2) - b^(2)),(2ab) is a pythagorean triplet. Find two Pythagorean triplets using any convenient values of a and b.

M.A. is always greater than 1 in

If a and b are natural numbers and a gt b, then show that (a^(2)+b^(2)),(a^(2)-b^(2))_,(2ab) is a Pythagorean triplet. Find two Pythagorean triplets using any convenient values of a and b.

A triplet (mnp) of three natural numbers mn and p is called a pythagorean triplets if m^(2)+n^(2)=p^(2)

If n is odd number and n>1 then prove that (n,(n^(2)-1)/(2),(n^(2)+1)/(2)) is a Pythagorean triplet.Write two Pythagorean triplet taking suitable value of n

For any natural number m, evaulate, int(x^(3m)+x^(2m)+x^(m))(2x^(2m)+3x^m+6)^(1//m)dx, x gt0

for what values of m, the equation 2x^(2) -2 ( 2m +1) x+ m ( m +1) = 0 m in R has (i) Both roots smallar than 2 ? (ii) Both roots greater than 2 ? (iii) Both roots lie in the interval (2,3) ? (iv) Exactly one root lie in the interval (2,3) ? (v) One root is smaller than 1, and the other root is greater than 1 ? (vi) One root is greater than 3 and the other root is smaller than 2 ? (vii) Roots alpha and beta are such that both 2 and 3 lie between alpha and beta ?

Suppose m and n are any two numbers . If m^(2) -n^(2) , 2mn and m^(2) + n^(2) are the three sides of a triangle , then show that it is a right angled triangle and hence write any two pairs of Pythagorean triplet .