Question

Using the formula n2 = (n + 1)(n-1) + 1 find the square of (i) 14 (ii) 27
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Answer 1

Answer:

• 14² = 196
• 27² = 729

Step-by-step explanation:

★ Given formula:

n² = [(n + 1) (n - 1)] + 1

★ Solution:

For finding 14 square;

n² = [(n + 1) (n - 1)] + 1

⇒ 14² = [(14 + 1) (14 - 1)] + 1

⇒ 14² = [(15) (13)] + 1

⇒ 14² = 195 + 1

⇒ 14² = 196

∴ (14)² = 196

For finding 27 square;

n² = [(n + 1) (n - 1)] + 1

➝ 27² = [(27 + 1) (27 - 1)] + 1

⇒ 27² = [(28) (26)] + 1

⇒ 27² = [28 × 26] + 1

⇒ 27² = 728 + 1

⇒ 27² = 729

∴ (27)² = 729

Answer 2

$\sf\huge\bold{Answer:}$

Given :

formula n² = (n + 1)(n-1) + 1

To find :

1. 14²
2. 27²

Solution :

Case:1

14²

n² = (n + 1)(n-1) + 1

14²=(14+1)(14-1)+1

14²=(15)(13)+1

14²=195+1

14²=196

Case:2

27²

n² = (n + 1)(n-1) + 1

27²=(27+1)(27-1)+1

27²=(28)(26)+1

27²=728+1

27²=729