Question

If \(tanA\) and \(tanB\) are the roots of the equation \(5x^2-4x+1 = 0\), then the value of \(A+B\) is...

• A. \(\frac{π}{6}\)
• B. \(\frac{π}{4}\)
• C. \(\frac{π}{3}\)
• D. \(\frac{π}{2}\)

Hint:

Convert 1/log_a b into log_b a and use the Pythagoras relation.

Answer 1

The Correct Option is B

Step 1: Take a numerical example:
Take the 3-4-5 triangle with $x = 3$, $y = 4$, $z = 5$. Then $x + z = 8$ and $z - x = 2$.

Step 2: Evaluate:
\[ \log_4 8 + \log_4 2 = \frac{3}{2} + \frac{1}{2} = 2 \]
since $4^{3/2} = 8$ and $4^{1/2} = 2$. The same value comes out in general, so the answer is (B).

Final Answer:
The expression equals 2. \[ \boxed{2} \]