Question

if x=2+√3,find the value of x^2+1÷x^2​

Answer 1

Answer:

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Answer 2

Given

if x=2+√3,find the value of x^2+1÷x^2

Solution

• x = 2 + √3

→ 1/x = 1/2 + √3

★Rationalise its denominator

→ 1/x = 1/2 + √3 × 2 - √3/2 - √3

→ 1/x = 2 - √3/(2)² - (√3)²

→ 1/x = 2 - √3/4 - 3

→ 1/x = 2 - √3

Now, the value of x² - 1/x²

• x = 2 + √3
• 1/x = 2 - √3

→ x² - 1/x²

→ (2 + √3)² + (2 - √3)²

★Apply identity :

(a + b)² = a² + b² + 2ab

(a - b)² = a² + b² - 2ab

→ (2)² + (√3)² + 2*2*√3 + 2 + (2)² + (√3)² - 2*2*√3 + 2

→ 4 + 3 + 4√3 + 4 + 3 - 4√3

→ 8 + 6

→ 14

Hence, the value of x² - 1/x² is 14