The expression (12.86 × 12.86 + 12.86 × p + 0.14 × 0.14) will be a perfect square for p equal to

Question

The expression (12.86 × 12.86 + 12.86 × p + 0.14 × 0.14) will be a perfect square for p equal to

A. 0

B. 0.28

C. 0.26

D. 1

Answer: B. 0.28

Solution:

(a+b)² = a²+2ab+b²

12.86 × 12.86 + 12.86 × p + 0.14 × 0.14

= (12.86)² + 12.86 × p + (0.14)²

This can be written as (12.86 + 0.14)² = 132,

if 12.86 × p = 2 × 12.86 × 0.14

i.e., if p = 2 × 0.14 = 0.28

Hence, p = 0.28 is the answer