Question : Simplify: $\frac{(3.321)^{3}+(2.681)^{3}+(1.245)^{3}–3×3.321×2.681×1.245}{(3.321)^{2}+(2.681)^{2}+(1.245)^{2}–(3.321×2.681)–(2.681×1.245)–(1.245×3.321)}=\ ?$
Option 1: 6.125
Option 2: 8.645
Option 3: 7.247
Option 4: 10.245
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Correct Answer: 7.247
Solution :
Given: $\frac{(3.321)^{3}+(2.681)^{3}+(1.245)^{3}–3×3.321×2.681×1.245}{(3.321)^{2}+(2.681)^{2}+(1.245)^{2}–(3.321×2.681)–(2.681×1.245)–(1.245×3.321)}$
We can say that this expression is in form of $\frac{a^{3}+b^{3}+c^{3}–3abc}{a^{2}+b^{2}+c^{2}–ab–bc–ca}=a+b+c$
Where, $a=3.321$, $b=2.681$, $c=1.245$
Then, $a+b+c=3.321+2.681+1.245=7.247$
Hence, the correct answer is 7.247.
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