Question

if x=√5+2,then x-1/x​

Answer 1

Answer:

X - 1/x

(root 5+2 )- ( 1×root5-2/ 5-4)

root5+2 - root 5-2

2 root 5

Answer 2

ANSWER:

• Value of the above expression = 2√5.

GIVEN:

$\implies \: x = \sqrt{5} + 2$

TO FIND:

• x -1/x

SOLUTION:

=> x = √5 +2

$\implies \: \dfrac{1}{x} = \dfrac{1}{ \sqrt{5} + 2} \\ \\ \implies \: \dfrac{1}{x} = \dfrac{1}{ \sqrt{5} + 2 } \times \dfrac{ \sqrt{5 } - 2}{ \sqrt{5} - 2} \\ \\ \implies \: \dfrac{1}{x} = \dfrac{ \sqrt{5} - 2 }{5 - 4} \\ \\ \implies \: \dfrac{1}{x} = \sqrt{5} - 2$

Finding (x +1/x)

= √5+2+√5-2

= 2√5

Value of the above expression = 2√5.

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