Question

if x= 2+√3 then x+1/x equals​

Answer 1

Solution:

Given –

→ x = 2 + √3

So,

→ 1/x = 1/(2 + √3)

Multiplying both numerator and denominator by (2 - √3), we get,

→ 1/x = (2 - √3)/[(2 + √3)(2 - √3)]

→ 1/x = (2 - √3)/(4 - 3)

→ 1/x = 2 - √3

Therefore,

→ x + 1/x = 2 + √3 + 2 - √3

→ x + 1/x = 4

★ So, the value of x + 1/x is 4.

Answer:

• x + 1/x = 4.

Answer 2

See the attachment for your help:-

GIVEN:−

x = 2 + √3

1/x = 1/(2 + √3) * (2 - √3)/(2 - √3)

1/x = (2 - √3)/(4 - 3)

[ (a - b)(a + b) = (a² - b²) ]

1/x = (2 - √3)

now,

x + 1/x = (2 + √3) + (2 - √3)

x + 1/x = 2 + 2 + √3 - √3

x + 1/x = 4.

$verified \: answer$