Question

if (a-1/a)=5, find the value of (a⁴+1/a⁴)​

Answer 1

Given ,

a+(1/a)=5

On squaring both sides we get,

[a+(1/a)]²= 25

a²+(1/a)²+2=25

a²+(1/a)²=23

Again squaring both sides,

[a²+(1/a)²]²=(23)²

a⁴+(1/a)⁴+2=529

a⁴+(1/a)⁴=527

Therefore answer is 527.

Answer 2

Answer :-

Therefore answer is 527.

explaination :-

Here a + 1/a = 5 is given,

Let we do square on both sides

(a + 1/a)² = 5²

a² + 1/a² + 2(a²)(1/a²) = 25

a² + 1/a² = 25 - 2

a² + 1/a² = 23

Again, doing square on both sides

(a² + 1/a²)² = 23²

a⁴ + 1/a⁴ + 2(a⁴)(1/a⁴) = 529

a⁴ + 1/a⁴ = 529 - 2

Hence,

a⁴ + 1/a⁴ = 527.

Hope its help..