Question

help fast .no spams please.all the parts ​

Answer 1

Answer:

i) 3-√7

ii) 6

iii) 32

Explanation:

i) 1/x = 1/(3+√7)/2 = 2/(3+√7)

= 2(3-√7)/(3+√7)(3-√7)

= 2(3-√7)/9-7 = 2(3-√7)/2

= 3-√7

ii) 2x+1/x

Now, 2x = 2((3+√7)/2) = 3+√7,

1/x = 3-√7

2x + 1/x = 3+√7 + (3-√7 ) = 6

iii) 4x² + 1/x² = (2x+1/x)² - 4 ....(1)

Now in equation (1) we put 2x = 3+√7 and 1/x = 3-√7

4x² + 1/x² = (2x+1/x)² - 4

=  {(3+√7 ) +(3-√7 )}²  -4

= (6)² -4=36-4 =32