Question

if x=5-2√6 then find value of x+1/x

Answer 1

Heya ✋

Let see your answer !!!!!

Given that

x = 5 - 2√6

x + 1/x = ?

Solution

1/x = 1/5 - 2√6

= 1 × 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

Hence ,

x + 1/x

= 5 - 2√6 + 5 + 2√6

= 10

Thanks :))))

Answer 2

Given,
x=5-2√6
1/x=1/5-2√6 ( Now, rationalize the denominator)
=1(5+2√6)/(5-2√6)(5+2√6)
=5+2√6/(5)^2-(2)^2*(√6)^2
=5+2√6/25-24
1/x=5+2√6

x+1/x= 5-2√6+5+2√6
= 5+5
= 10

Hope it helps.....