Question

Find the pythagorean triplet whose greatest number is 22​

Answer 1

GIVEN :

• The greatest number of a pythagorean triplet is 22.

TO FIND :

• The Pythagorean triplet.

SOLUTION :

Pythagorean triplet can be written as :

• 2n
• n² - 1
• n² + 1

Given, the greatest number = 22.

Now,

→ n² + 1 = 22

→ n² = 22 - 1

→ n² = 21

→ $\sf {\sqrt {21}}$

→ n = 4.58

Now, let's calculate for the other two numbers,

→ 2n = 2 (√21) = 2√21

→ n² - 1 = (√21) -1 = 20

→ n² + 1 = (√21) + 1 = 22.

VERIFICATION :

→ (22)² = (2√21) + 20

→ 484 = 84 + 400

→ 484 = 484

$\therefore$ LHS = RHS .

$\therefore$ Hence verified.

Answer 2

Answer:

GIVEN :

The greatest number of a pythagorean triplet is 22.

TO FIND :

The Pythagorean triplet.

SOLUTION :

Pythagorean triplet can be written as :

2n

n² - 1

n² + 1

Given, the greatest number = 22.

Now,

→ n² + 1 = 22

→ n² = 22 - 1

→ n² = 21

→ \sf {\sqrt {21}}

21

n = 4.58

Now, let's calculate for the other two numbers,

→ 2n = 2 (√21) = 2√21

→ n² - 1 = (√21) -1 = 20

→ n² + 1 = (√21) + 1 = 22.

VERIFICATION :

→ (22)² = (2√21) + 20

→ 484 = 84 + 400

→ 484 = 484

\therefore∴ LHS = RHS .

\therefore∴ Hence verified.