Discussion
If \(a - b = \frac{11}{5}\) and \(ab = \frac{3}{4}\), then one of the values of \((a + b)\) is :
Answer: B
One value of \((a + b)\) is \(2\frac{4}{5}\).
Use the identity linking the sum and difference of two numbers with their product.
\[ \begin{aligned} (a + b)^{2} &= (a - b)^{2} + 4ab \\ &= \frac{121}{25} + 4 \times \frac{3}{4} \\ &= \frac{121}{25} + \frac{75}{25} = \frac{196}{25} \end{aligned} \]
So \(a + b = \pm \frac{14}{5}\), and one of the values is \(\frac{14}{5} = 2\frac{4}{5}\). The question says 'one of the values' because \(-\frac{14}{5}\) also works. Forgetting the factor 4 on \(ab\) gives \(\sqrt{121/25 + 3/4}\), which is none of the options.
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