Question

If \[ \frac{\sqrt{11} - \sqrt{120}}{\sqrt{11} + 6\sqrt{2}} = A\sqrt{6} + B\sqrt{5} + C\sqrt{3} + D\sqrt{10}, \text{ then the value of } (A + B + C + D) \text{ is:} \]

• A. \(- \frac{2}{7} \)
• B. \(- \frac{1}{7} \)
• C. \(- \frac{1}{11} \)
• D. \(\frac{3}{11} \)

Hint:

When dealing with irrational numbers in equations, rationalize the denominator first before comparing the terms.

Answer 1

The Correct Option is B

To solve this, we need to rationalize the denominator and then equate the terms on both sides of the equation to find the values of \( A \), \( B \), \( C \), and \( D \). After simplifying the terms, the value of \( (A + B + C + D) \) comes out to be \( - \frac{1}{7} \).