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# Discussion

The expression $$(12.86 \times 12.86 + 12.86 \times p + 0.14 \times 0.14)$$ will be a perfect square for $$p$$ equal to:

• A.0.28
• B.0.26
• C.1
• D.0

$$(a + b)^2 = a^2 + 2ab + b^2$$
$$12.86 \times 12.86 + 12.86 \times p + 0.14 \times 0.14$$
$$= (12.86)^2 + 12.86 \times p + (0.14)^2$$
This can be written as,
$$(12.86 + 0.14)^2 = 13^2$$
If, $$12.86 \times p = 2 \times 12.86 \times 0.14$$
i.e., if $$p = 2 \times 0.14 = 0.28$$

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