What is the value of \(\displaystyle\frac{(6.3)^{3}+(3.7)^{3}}{(6.3)^{2}-6.3\times3.7+(3.7)^{2}}\)?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 10
The sum of two cubes factorises as \(a^{3}+b^{3}=(a+b)(a^{2}-ab+b^{2})\). The denominator is the second factor, so the fraction equals \(a+b\).
\(a=6.3,\ b=3.7\)
\(\displaystyle\frac{(a+b)(a^{2}-ab+b^{2})}{a^{2}-ab+b^{2}}=a+b\)
\(a+b=6.3+3.7=10\)