Question : Simplify: $\frac{(0.73)^3+(0.27)^3}{(0.73)^2+(0.27)^2-0.73\times 0.27}$
Option 1: 1
Option 2: 0.4087
Option 3: 0.73
Option 4: 0.27
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Correct Answer: 1
Solution :
Since a
3
+ b
3
= (a + b)(a
2
+ b
2
– ab),
So, $\frac{(0.73)^3+(0.27)^3}{(0.73)^2+(0.27)^2-0.73\times 0.27}$
= $\frac{(0.73+0.27) [(0.73)^2+(0.27)^2-0.73\times 0.27]}{(0.73)^2+(0.27)^2-0.73\times 0.27}$
= 0.73 + 0.27
= 1
Hence, the correct answer is 1.
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