Question

if a+1/a=3 then a^4+1/a^4=?​

Answer 1

(a+1/a)power4 is 81.

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Answer 2

Answer:

Note:

(A+B)^2 = A^2 + B^2 + 2•A•B

Given:

a +1/a = 3

To find:

a^4 + 1/a^4 = ?

Solution:

Here, we have;

a +1/a = 3 --------(1)

Also, we know that;

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

=> (3)^2 = a^2 +1/a^2 + 2 {using eq-1}

=> 9 = a^2 + 1/a^2 + 2

=> a^2 + 1/a^2 = 9 - 2

=> a^2 + 1/a^2 = 7 ---------(2)

Again;

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

+ 2•(a^2)•(1/a^2)

=> (7)^2 = a^4 +1/a^4 + 2 {using eq-2}

=> 49 = a^4 + 1/a^4 + 2

=> a^4 + 1/a^4 = 49 - 2

=> a^4 + 1/a^4 = 47

Hence,

The required value of a^4 + 1/a^4 is;

47.