Question

If x⁴+ 1/x⁴ = 623, then x + 1/x =
A. 27
B. 25
C. 3√3
B. -3√3

Answer 1

Given : x⁴ + 1/x⁴ = 623

 

To find : value of  x + 1/x

 Solution :  

We know that  

(x² + 1/x² )² = (x²)² + (1/x²)² + 2 x² × 1/x²

(x² + 1/x² )² = x⁴ + 1/x⁴ + 2

(x² + 1/x² )² = 623 + 2

(x² + 1/x² )² = 625

(x² + 1/x² )² = 25²

x² + 1/x²  = 25……….(1)

[Taking square root of both sides]

Now ,

we know that (x + 1/x)² = x² + 1/x² + 2

(x + 1/x)² = 25 + 2

[From eq 1]

(x + 1/x)² = 27

(x + 1/x)² = 27²

x + 1/x = 3√3

Hence the value of x + 1/x is  3√3.

Among the given options option (C) 3√3 is correct.

HOPE THIS ANSWER WILL HELP YOU…..

 

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Answer 2

Step-by-step explanation:

If x⁴+ 1/x⁴ = 623, then x + 1/x =

A. 27

B. 25

C. 3√3

B. -3√3✔️