Question

If x+1/x= √5, what are the values of x²+1 /x² and x⁴ + 1 /x⁴?​

Answer 1

Answer:

6 and 26 is the right answer

Answer 2

Step-by-step explanation:

Given:-

x+1/x= √5

To find:-

If x+1/x= √5, what are the values of x²+1 /x² and

x⁴ + 1 /x⁴?

Solution:-

Given equation is x+1/x=√5

On squaring both sides ,then

=>(x+1/x)²=(√5)²

=>x²+2(x)(1/x)+(1/x)²=5

=>x²+2+1/x²=5

=>x²+1/x²=5-2

Therefore,x²+1/x²=3

Again ,on squaring both sides then

=>(x²+1/x²)²=3²

=>(x²)²+2(x²)(1/x²)+(1/x²)²=9

=>x⁴+2+1/x⁴=9

=>x⁴+1/x⁴=9-2

Therefore,x⁴+1/x⁴=7

Answers:-

1)The value of x²+1/x²=3

2)The value of x⁴+1/x⁴=7

Used formula:-

• (a+b)²= a²+2ab+b²