Question

plllllzzz give solllllllutioun

Answer 1

second method ------> SECOND ATTACHMENT

Answer 2

Final Result :

${x}^{r} + \frac{1}{ {x}^{r} } \: = 2 \\ where \: r \: belongs \: to \: real \: number.$

Concepts to know :

1 ) Arithmetic Mean >=Geometric Mean

Or Frankly Speaking :

(a + b) /2 >=√(ab) , where a, b >=0 and belongs to R.

=> Min value of (a + b) /2 is √(ab) when a = b

Steps :

1) Here, a = x and b = 1/x .
then min value of

(x + 1/x ) is 2 .
when x = 1. .

2) From, here final general result can be obtained.

That is,

${x}^{r} + \frac{1}{ {x}^{r} } \: = 2 \\ where \: r \: belongs \: to \: real \: number.$

Hope, you understand my answer .