Question : Simplify the given expression: $\frac{(0.25)^4+2×(0.25)^2+1–(0.25)^2}{(0.25)^2+0.25+1}$
Option 1: 0.6755
Option 2: 0.9025
Option 3: 0.8125
Option 4: 0.7835
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Correct Answer: 0.8125
Solution :
Given:
$\frac{(0.25)^4+2×(0.25)^2+1–(0.25)^2}{(0.25)^2+0.25+1}$
= $\frac{((0.25)^2+1)^2–(0.25)^2}{(0.25)^2+0.25+1}$
= $\frac{((0.25)^2+1+0.25)((0.25)^2+1–0.25)}{(0.25)^2+0.25+1}$
= $\frac{((0.25)^2+0.25+1)((0.25)^2+1–0.25)}{(0.25)^2+0.25+1}$
= $0.25^2 + 1 - 0.25$
= $0.0625 + 0.75$
= $0.8125$
Hence, the correct answer is 0.8125.
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