Question

If x= 3 + under root 8 then the value of x2 + 1 upon x2 is equal to

Answer 1

Answer:

given, x= 3+√8

to find the value of x^2 + 1/x^2

first find the reciprocal of x and rationalize its denominator by its conjugate

therefore 1/x = 1/(3+√8) * (3-√8)/(3-√8)

=> (3-√8)/(3^2 - (√8)^2) [ a^2 - b^2 = (a+b)(a-b) ]

=> 3-√8/9-8

=> 3-√8

now x + 1/x = 3+√8+3-√8

=> x + 1/x = 6 [ √8 cancels out ]

=> (x + 1/x)^2 = 36

=> x^2 + 1/x^2 + x*1/x*2 = 36

=> x^2 + 1/x^2 + 2 = 36

therefore x^2 + 1/x^2 = 36 - 2

= 34............ Answer