Question

If x = under root 31 + 8 root 15 find x+1/x

Answer 1

Given: x = √(31 + 8√15)

To find: The value of x + 1/x

Solution:

• Now we have x = √(31 + 8√15)

• Lets rewrite √(31 + 8√15) as :

           x = √(31 + 2√ 15 x 4 x 4)

           x = √( 31 + 2 √ 15 x 16 )

           x = √{ (√16)^2 + (√15)^2 + 2×(√16)(√15) }

• Now it becomes the square term:

            x = √( √16 + √15)^2

           x = √16 + √15

           x = 4 + √15

• Now putting this value in x + 1/x, we get:

            4 + √15  + 1/ 4 + √15

           (4 + √15  )^2 + 1 / 4 + √15  

          16 + 15 + 8√15 + 1 / 4 + √15  

           32 + 8√15 / 4 + √15  

           4 + √15  

Answer:

       So the value of x + 1/x is 4 + √15  

Answer 2

√[31 + 8√15]

√[31 + 2 √ 15×16]

√ 【(√16)^2 + (√15)^2 + 2×(√16)(√15)】

√[( √16 + √15) ^2 ]

√16 + √15

4 + √15