Question

If x=2+root3 then x-1/x is equal to

Answer 1

Answer:

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Answer 2

GIVEn

If x=2+√3 then

find the value of x - 1/x

SOLUTIOn

• x = 2 + √3
• 1/x = ?

→ 1/x = 1/2 + √3

★ Rationalize its denominator

→ 1/x = 1/2 + √3 × 2 - √3/2 - √3

★ Apply identity :

a² - b² = (a + b)(a - b)

→ 1/x = 2 - √3/(2)² - (√3)²

→ 1/x = 2 - √3/4 - 3

→ 1/x = 2 - √3

Now, the value of x - 1/x

→ x - 1/x

→ 2 + √3 - (2 - √3)

→ 2 + √3 - 2 + √3

→ √3 + √3

→ √3(1 + 1)

→ 2√3

Hence, the value of x - 1/x is 2√3