First slide

Properties of triangles

Question

$Let f (x + y) = f (x) f (y) for all x and y and f (1) = 2 . If in a triangle ABC, a = f (3), b = f(1) + f(3), c = f(2) + f(3) then 2A is equal to$

Moderate

A

C
B

2C
C

3C
D

4C

Solution

$\begin{array}{l} f (x + y) = f (x) f (y) \\ \Rightarrow f (x) = a^{x} \\ f (1) = 2 \Rightarrow a = 2 \\ \Rightarrow f (x) = 2^{x} \\ \Rightarrow a = 8, b = 10, c = 12 \\ \cos A = \frac{3}{4} \\ Cos 2 A = 1 / 8, \cos C = 1 / 8 \\ ∴ 2 A = C \end{array}$

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