Question

[(9.6)³-0.343]/[(9.6)²+6.72+0.49] + [(2.6)³-0.008]/[(2.6)²+0.52+0.04]

• A. 12.12
• B. 45.70
• C. 11.3
• D. 765.25

Hint:

Apply the trapezium area formula with the given parallel sides and height.

Answer 1

The Correct Option is C

Both fractions here follow the pattern of the algebraic identity \(a^3 - b^3 = (a-b)(a^2 + ab + b^2)\), where the denominator matches the \((a^2+ab+b^2)\) part of the identity exactly, so each fraction collapses down to simply \((a-b)\).
For the first term, \(a=9.6\) and \(b=0.7\) (since \(0.343=0.7^3\)), giving \(9.6-0.7=8.9\). For the second, \(a=2.6\) and \(b=0.2\) (since \(0.008=0.2^3\)), giving \(2.6-0.2=2.4\).
Adding these two simplified terms gives \(8.9+2.4=11.3\), matching option 3.