Question

x=2-√7/3 find x²+1/x² step by step​

Answer 1

Answer:

1/9

Step-by-step explanation:

x=(2-√7/3)

x^2-1/x^2:

x^2=(2-√7/3)^2

=(a-b)^2

=a^2+b^2-2ab

=2^2+(√7/3)^2-2*2*√7/3

=4+7/9-2*2*√7/3

by taking LCM of denominator...we get

=36+7/9-4√7/3

=43/9-4√7/3

now again taking the LCM.............we get

=43-12√7/9..............(1)

now x^2+1/x^2=(43-12√7)/9+1/(43+12√7)/9

now changing the signs we get,

=43-12√7+(-43+12√7)/9

=1/9..…..ans