Question

if x=3+√8 , find the value of x+1/x​

Answer 1

Step-by-step explanation:

just put in this equation u get urs answer perfectly

u get

9+8+1/3+root8

18/3+root8 by multiplying it's conjugate u get urs answer

Answer 2

ANSWER:

• Value of the above expression = 6.

GIVEN:

• x = 3+√8.

TO FIND:

• Value of x+1/x.

SOLUTION:

=> x = 3+√8

$\implies \: \dfrac{1}{x} = \dfrac{1}{3 + \sqrt{8} } \\ \\ \implies \: \dfrac{1}{x} = \dfrac{1}{3 + \sqrt{8} } \times \dfrac{3 - \sqrt{8} }{3 - \sqrt{8} } \\ \\ \implies \: \dfrac{1}{x} = \dfrac{3 - \sqrt{8} }{9 - 8} \\ \\ \implies \: \dfrac{1}{x} = 3 - \sqrt{8}$

Now :

= x+ 1/x

= 3+√8 +3-√8

= 6

Value of the above expression = 6.

NOTE:

Some important formulas:

(a+b)² = a²+b²+2ab

(a-b)² = a²+b²-2ab

(a+b)(a-b) = a²-b²

(a+b)³ = a³+b³+3ab(a+b)

(a-b)³ = a³-b³-3ab(a-b)

a³+b³ = (a+b)(a²+b²-ab)

a³-b³ = (a-b)(a²+b²+ab)

(a+b)² = (a-b)²+4ab

(a-b)² = (a+b)²-4ab