Question:
<p>Two sides a and b of triangle ABC are given by the roots of the equation x<sup>2</sup> - 4x + 1 = 0 and the included angle between them is <span class="math-tex">\(\frac{\pi}{3}\)</span> then the value of <span class="math-tex">\(\left(\frac{c^{2}}{a+b}\right)\)</span> is :</p>
<p style="display:inline"><span class="math-tex">\(\frac{4}{13}\)</span></p>
<p style="display:inline">4</p>
<p style="display:inline"><span class="math-tex">\(\frac{13}{4}\)</span></p>
<p style="display:inline"><span class="math-tex">\(\frac{1}{4}\)</span></p>
Step-by-Step Solution
Key Concept: Use Vieta's formulas to determine the sum and product of sides a and b, then apply the Law of Cosines to find c².
<p><span class="math-tex">\(\frac{13}{4}\)</span></p>
Correct Answer: C