Question

If x = √5 + 2, then x-1/x equals
4
3
2
1​

Answer 1

Answer:

x - 1/x = 4

Step-by-step explanation:

x = √5 + 2

Then, 1/x = 1/(√5 + 2)

x - 1/x

(√5 + 2) - 1/(√5 + 2)

[(√5 + 2)(√5 + 2) - 1] / (√5 + 2)

[(5 + 2√5 + 2√5 + 4) - 1] / (√5 + 2)

(9 + 4√5 - 1) / (√5 + 2)

(8 + 4√5) / (√5+2)

4(2+√5) / (√5+2)

4

OR

x = √5 + 2

x - 2 = √5

Squaring both sides,

(x-2)² = (√5)²

x² + 4 - 4x = 5

x² - 4x = 5 - 4

x² - 4x = 1

x² - 1 = 4x

Dividing x both sides,

x - 1/x = 4