What is the value of \(\frac{{{{\left( {1.2} \right)}^3} + {{\left( {0.8} \right)}^3} + {{\left( {0.7} \right)}^3} - 2.016}}{{\left( {1.35} \right)\left[ {{{\left( {1.2} \right)}^2} + {{\left( {0.8} \right)}^2} + {{\left( {0.7} \right)}^2} - 0.96 - 0.84 - 0.56} \right]}}?\)
2
Let \(a=1.2,\ b=0.8,\ c=0.7\). Then \(3abc=2.016\) and \(ab+bc+ca=0.96+0.56+0.84\), so the bracket equals \(a^2+b^2+c^2-ab-bc-ca\).
Apply the identity:
\[a^3+b^3+c^3-3abc=(a+b+c)(a^2+b^2+c^2-ab-bc-ca)\]
The bracket cancels, leaving \(\dfrac{a+b+c}{1.35}=\dfrac{2.7}{1.35}=\mathbf{2}\).
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