Question

i) How many natural numbers lie between the squares of 16 and 17. ii) Write a Pythagorean triplet whose one number is 18.​

Answer 1

Answer:

i) 32 numbers

ii) 18 is the Pythagorean triplet of 80 and 82.

Step-by-step explanation:

i) Between 16 and 17, there are 2×16=32 i.e. 32 numbers

ii) We have pythagorean triplet (2n,n2−1,n2+1) where n>1 (natural number)

Let n2−1=18

n2=19

n=19 (not an integer)

n2+1=18

n2=18−1

n2=17

n=17 (is not an integer)

So, let us take 2n=18

n=9

∴ The required triplet is (an integer)

(18,92−1,92+1)=(18,81−1,81+1)

i.e., (18,80,82)

Hope it helps u