Question

if x =5 -2√6,find x²+1/x²​

Answer 1

Answer:

102

Step-by-step explanation:

x= 5-2√6

1/x = 1/5-2√6

= 5+2√6/(5-2√6)(5+2√6)

= 5+2√6/(5)^2 - (2√6)^2

=5+2√6/25-24

= 5+2√6/1

= 5+2√6

x+1/x = 5+2√6+5-2√6

= 10

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

=10^2+2

= 100+2

=102

Answer 2

Answer:

we know that x = 5 -2√6

so 1/x =1/5-2√6

now we rationalise the 1/5-2√6

so after rationalise we get 1/x = 5+2√6

now we find the value of x+1/x

5-2√6 + 5+2√ 6

so the answer or value of x+1/x is 10

now x+1/x = 10

now squaring on both side

(x+1/x)^2 = (10)^2

now (a+ b)^2 = a^2+ b^2+2ab

so like this x^2 + (1/x)^2 +2*x*1/x = 100

now. x^2+ 1/x^2 +2 = 100

x^2 + 1/x^2 = 98

hope it will help you