Question

What are the roots of the equation 4^x – 3.2^{x + 2} + 32 = 0 ?

(a) 1, 2 

(b) 3, 4 

(c) 2, 3 

(d) 1, 3

Answer 1

(c) 2, 3

4^x – 3.2^{x + 2} + 32 = 0 

⇒ 2^2x – 3.2².2^x + 32 = 0 ⇒ 2^2x – 12.2^x + 32 = 0 

Let 2^x = a. Then, a² – 12a + 32 = 0 

⇒ (a – 8) (a – 4) = 0 ⇒ a = 8 and 4 ⇒ 2^x = 8 and 2x = 4 ⇒ x = 3 and x = 2