Question

If x=233 + 88√7 then what will be the value of x power 1/4 - 3x power -1/4

Answer 1

Step-by-step explanation:

x = 233 + 88sqrt(7)

To find:

The value of x ^ (1/4) - 3x ^ (- 1/4)

Solution:

Consider,

x = 233 + 88sqrt(7)

x = 121 + 112 + 88sqrt(7)

x = 11 ^ 2 + (4sqrt(7)) + 2(11)(4sqrt(7))

x = (11 + 4sqrt(7)) ^ 2

x = (4 + 7 + 4sqrt(7)) ^ 2

x = (2 ^ 2 + sqrt^2 7 + 2(2)(sqrt(7))) ^ 2

x = ((2 + sqrt(7)) ^ 2) ^ 2

x = (2 + sqrt(7)) ^ 4

x₁ = 2 + √7