Question

find the Pythagorean triplet in which one number is 20
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Answer 1

For any natural numbers m>1,2m, m2−1, m2+1 forms a Pythagorean triplet.

If we take m2+1=20, then m2=19

The value of m will not be an integer.

If we take m2−1=20, then m2=21

Again the value of m will not be an integer.

Let 2m=20

=>m=10

∴2m=2⋅10=20

m2−1 = 102−1=99

and

m2+1 = 102+1=101

Therefore, the Pythagorean triplets are 20,99,101.

Answer 2

✪ Question ✪

Find the Pythagorean triplet in which one number is 20.

✪ To find ✪

The Pythagorean triplet.

✪ Pythagorean Triplet ✪

A Pythagorean Triplet with x:-

{2x, (x²-1), (x²+1)}

✪ Solution ✪

Consider that 20 is the smallest member of the triplet.

According to the triplet with x,

2x = 20

We have to find x.

2x = 20

⇒x = 20/2

⇒x = 10

So, x = 10.

• (x²-1)

= (10²-1)

= (100-1)

= 99

• (x²+1)

= (10²+1)

= (100+1)

= 101

✪ Hence ✪

2x = 20

(x²-1) = 99

(x²+1) = 101

The Pythagorean triplet = (20, 99, 101)

✪ Therefore ✪

The Pythagorean triplet in which one number is 20 is (20, 99, 101).

๑ Hope this helps you. ๑