Question

if x=2+√5 find x^2-1/x^2

Answer 1

Answer:

If x= 2+sqrt3

If x= 2+sqrt3then

If x= 2+sqrt3then1/x=2-sqrt3 (by rationaliztion)

If x= 2+sqrt3then1/x=2-sqrt3 (by rationaliztion)then (x+1/x)^2 = X^2+(1/X)^2 +2*x*(1/X)

If x= 2+sqrt3then1/x=2-sqrt3 (by rationaliztion)then (x+1/x)^2 = X^2+(1/X)^2 +2*x*(1/X)that is (2+sqrt3 +2-sqrt3)^2=x^2 +(1/x)^2+2

If x= 2+sqrt3then1/x=2-sqrt3 (by rationaliztion)then (x+1/x)^2 = X^2+(1/X)^2 +2*x*(1/X)that is (2+sqrt3 +2-sqrt3)^2=x^2 +(1/x)^2+24^2 -2=x^2+(1/x)^2

If x= 2+sqrt3then1/x=2-sqrt3 (by rationaliztion)then (x+1/x)^2 = X^2+(1/X)^2 +2*x*(1/X)that is (2+sqrt3 +2-sqrt3)^2=x^2 +(1/x)^2+24^2 -2=x^2+(1/x)^2i.e, 14 is the answer

Answer 2

Step-by-step explanation:

= 2+root5

x2 = (2+root5)2 =9 +4root5 {using identity (a+b)2}

1/x2  = (1/2+root5 )2  =1/9 +4root5 

so x2 +1/x2    = 9+4root5 + 1/9+4root5

                      =9+4root5 + 9- 4 root5 

                                          (9)2  - (4root5)2

                      =9 +4root5 +9 -4root5 

                                             1

                     9+4root5 +9 - 4root5  =18

thus x2 +1/x2 =18 proved