Question

if x = 2 + √3, then find the value of x^2+1/x^2.
pls tell answer fast I'll mark it brainliest​

Answer 1

Answer:

here you go my friend

Step-by-step explanation:

given:-

x = 2 + √3

1/x = 1/2 + √3

= 1 × (2-√3)/(2 + √3)(2-√3)

= (2-√3)/(2^2-√3^2)

= (2-√3)/4 - 3

= (2-√3)

Therefore,

x^2 = (2+√3)

= (2)^2 + (√3)^2 + 2 × 2 × √3

= 4 + 3+ 4√3

= 7+ 4√3

1/x^2=(2-√3)^2

= (2)^2 + (√3)^2 - 2×2× √3

= 4 + 3 - 4√3

= 7 - 4√3

x^2+1/x^2

= (7 + 4√3) + (7 - 4√3)7+ 4√3+7-4√3

= 7 + 7 + 4√3 - 4√3

= 14