Question

3
7. If x = 3 + 78, then find
the value of​

Answer 1

Answer:

x^2 + 1/x^2=34

Explanation:

Given :

x = 3+ √8

To find:

x^2 + 1/x^2

as x = 3+√8

x^2 = (3+√8)^2

x^2 = ((3)^2 + (√8) ^2 + 2(3) (√8))

x^2 = (9 + 8 + 6√8 )

x^2= 17 + 6√8

1/x^2 = 1 / 17 + 6√8

so now

x^2 + 1/x^2 = (17 + 6√8 ) + ( 1 / 17 + 6√8 )

x^2 + 1/x^2 = [(17+6√8) (17+6√8) + 1 ] / [17 + 6 √8]

x^2 + 1/x^2= [289+102√8+102√8+288+1] / [17+6√8]

x^2 + 1/x^2=[578+204√8] / [17+6√8]

x^2 + 1/x^2= 34[17+6√8] / [17+6√8]

x^2 + 1/x^2=34

Therefore the value of x^2 + 1/x^2 is 34