Question

If a + 1/ 16, then find the value of a^2 +1/a^2?​

Answer 1

Answer:

Correct question;

If ( a + 1/a) = 16 , then find the value of

a^2 + 1/a^2.

Note,

(a + b)^2 = a^2 + b^2 + 2•a•b

we can use this identity to find the value of a^2 + 1/a^2

Now;

=> (a+1/a)^2 = a^2 + (1/a)^2 + 2•a•(1/a)

=> (16)^2 = a^2 + 1/a^2 + 2

=> 256 = a^2 + 1/a^2 + 2

=> a^2 + 1/a^2 = 256 - 2

=> a^2 + 1/a^2 = 254

Thus, the required value of a^2 + 1/a^2 is 254.