Quadratic Equation

Question

Roots of 3^x + 3^-x = 10/3 are

(A) 0, 1

(B) 1, -1

(C) 0, -1

(D) None of these

Answer 1

3^x + 3^-x = 10/3

3^x + 1/3^x = 10/3

Let 3^x = k

K + 1/k = 10/3

\(\frac{k^ 2+1}{k}=\frac{10}{3}\)

3(k²+1) = 10k

3k² - 10k + 3 = 0

3k² - 9k - k + 3 = 0

3k(k-3) - 1(k - 3) = 0

(k-3) (3k-1) = 0

k = 3, 1/3

3^x = 3, 1/3

3^x = 3¹, 3^-1

x = 1, -1