Question

If x+1/x is equal to 6, find:1.x-1/x...... 2.x²-1/x²......3.x²+1/x²...???​

Answer 1

Answer:

Step-by-step explanation:

x + 1/x = 6

1. we know that (a - b)² = (a + b)² - 4ab

=> (x - 1/x)²  = (x + 1/x)² - 4(x)(1/x) = 6² - 4 = 32

=> x - 1/x = ±√32 = ±4√2

2. We know that a² - b² = (a + b)(a - b)

x² - 1/x² = (x + 1/x)(x - 1/x) = 6 * (±4√2) = ±24√2.

3. We know that a² + b² = (a + b)² - 2ab

x² + 1/x² = (x + 1/x)² - 2(x)(1/x) = 6² - 2 = 34.