Question

Please help- Number system class 9​

Answer 1

Answer:

x= root 5 - 2/ root 5 +2

rationalising the denominator

x= (root5-2) X (root5-2)/ (root5+2) X (root5-2)

x= 5- 2root5 - 2root5+4 / (root5)^2- (2)^2

x=9 -4root 5 / 5-4

x= 9 - 4root5  

1/x= 1/9-4root5

1/x= (1) X (9+4root5)/ (9-4root5) X (9+4root5)

1/x= 9+4root5/ (9)^2-(4root5)^2

1/x= 9+4root5/ 81-80

1/x= 9+4root5

(i) x+1/x=18

(9-4root5)+ (9+4root5)=18

9-4root5 +9+4root5 =18

18=18 [as positive 4root5 and negative 4root5 gets cancelled , then 9 +9=18]

Hence, proved