Question

Roots of 3^x+3^-x=10/3​

Answer 1

Answer:

-1 AND 1

Step-by-step explanation:

Answer 2

The roots of the equation 3^x + 3^-x = 10/3​ are 1 and -1.

Given: The equation 3^x + 3^-x = 10/3​

To Find: The roots of the equation 3^x + 3^-x = 10/3​.

Solution:

Let us take 3^x = t

So the equation becomes,

    t + 1/ t = 10/3

⇒  3t² - 10t + 3 = 0

⇒  3t² - 9t - t + 3 = 0

⇒  3t ( t - 3 ) - 1 ( t - 3 ) = 0

⇒  ( 3t - 1 ) ( t - 3 ) = 0

⇒  t = 3, 1/3

So, putting t = 3^x, we get;

     3^x = 3        and        3^x = 1/3

 ⇒ x = 1            and          x  = -1

Hence, the roots of the equation 3^x + 3^-x = 10/3​ are 1 and -1.

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