Question

If (x + 1/x) = 5,
Then find the value of
(x⁴ + 1/x⁴)​

Answer 1

Answer

x+1/x = 5

(x+1/x)? = x²+1/x²+2 (5)? = x²+1/x²+2 25-2 = x2+1/x2 => 23

(x²+1/x?)? = x*+1/x*+2

(23)2 = x*+1/x*+2

4 529-2 = x*+1/xª

527 = x4+1/x4

hope this helps

Answer 2

Step-by-step explanation:

Given :-

x + 1/x = 5

To find:-

If (x + 1/x) = 5, Then find the value of (x⁴ + 1/x⁴) ?

Solution:-

Given that:

x + 1/x = 5

On squaring both sides then

=>(x + 1/x)^2 = 5^2

It is in the form of (a+b)^2

Where , a= x and b = 1/x

we know that

(a+b)^2 = a^2 +2ab +b^2

=>x^2+2(x)(1/x) + (1/x)^2 = 25

=>x^2 + 2 + 1/x^2 = 25

=>x^2 + 1/x^2 = 25-2

=>x^2 + 1/x^2 = 23

again ,On squaring both sides

=>(x^2 + 1/x^2)^2 = 23^2

It is in the form of (a+b)^2

Where , a= x^2and b = 1/x^2

we know that

(a+b)^2 = a^2 +2ab +b^2

=>(x^2)^2 + 2(x^2)(1/x^2)+(1/x^2)^2 = 529

=>x^4+2 + 1/x^4 = 529

=>x^4 + 1/x^4 = 529-2

=>x^4 + 1/x^4 = 527

Answer:-

If (x + 1/x) = 5, the value of (x⁴ + 1/x⁴) = 527

Used formulae:-

• (a+b)^2 = a^2 +2ab +b^2
• (a^m)^n=a^mn