Question

if x=2+√3 then x^2-1/x^2​

Answer 1

Answer:

8√3

concept used:

x² -1/x² = (x + 1/x)(x - 1/x)

Step-by-step explanation:

given,

x = 2+√3

=> 1/x = 1/(2+√3) = (2-√3) / ((2+√3)(2-√3)) = 2-√3

=> x - 1/x = (2+√3) - (2-√3) = 2√3

=> x + 1/x = (2+√3) + (2-√3) = 4

so, x²-1/x² = (x +1/x)(x-1/x) = 2√3 × 4 = 8√3