Question

If x = root 5 - 2 / root 5 + 2
Find : x square + 1 / x square

Answer 1

Answer:

Heya ✋

Let see your answer !!!

Given that

x = 2 + √5

x^2 + 1/x^2 = ?

Solution

1/x = 1/2 + √5

By rationalization

= 1 × (2 - √5)/(2 + √5) × (2 - √5)

= 2 - √5/(2)^2 - (√5)^2

= 2 - √5/4 - 5

= 2 -√5/-1

= -2 + √5

Therefore ,

x^2 + 1/x^2

= (2 + √5)^2 + (-2 + √5)^2

= (2)^2 + (√5)^2 + 2 × 2 × √5 + (-2)^2 + (√5)^2 + 2 × (-2) × √5

= 4 + 5 + 4√5 + 4 + 5 - 4√5

= 9 + 4√5 + 9 - 4√5

= 18

Thanks :)

Answer 2

Step-by-step explanation:

step 1

x= root 5-2 /root 5 +2

rationalise the denominator

step 2

x= root 5-2/ root 5+2 ×root 5-2 / root 5-2

×=(root 5-2)^2/( root 5+2)(root 5 -2)

step 3

x= root 5^2+2^2-2×root 5 ×2 /(root5^2)-(2^2)

x= 5+4 - 4 root 5 /5-4

x=9-4 root 5

1/x = 1/9-4 root 5

step 4

x^2+1/x^2=9^2-4 root 5^2 +1/9-4root5^2

161+1/81-80

161+0

161

hope it helps u