Question

if x=3+√5\2,show that x+1\x=3. ​

Answer 1

We know that, (a+b)

3

=a

3

+b

3

+3ab(a+b)

x

3

+

x

3

1

=(2+

3

)

3

+

(2+

3

)

3

1

Here, taking (2+

3

)

3

⇒(2+

3

)

3

=2

3

+

3

3

+3×2×

3

(2+

3

)

=8+3

3

+6

3

(2+

3

)

=8+3

3

+12

3

+18

=26+15

3

Now, (2+

3

)

3

+

(2+

3

)

3

1

=26+15

3

+

26+15

3

1

Taking

26+15

3

1

⇒

26+15

3

1

×

26−15

3

26−15

3

=

676−675

26−15

3

=26−15

3

Now,

=26+15

3

+26−15

3

=52

Hence proved