Verified answer

4√2 & 24√2

Step-by-step explanation:

Square on both sides:

→ (x + 1/x)² = 6²

→ x² + 1/x² + 2(x*1/x) = 36

→ x² + 1/x² + 2(1) = 36

→ x² + 1/x² = 36 - 2 = 34

Subtract 2(x*1/x) from both sides:

→ x² + 1/x² - 2(x*1/x) = 34 - 2(x*1/x)

→ (x - 1/x)² = 34 - 2(1) = 32

→ x - 1/x = √32 = √(16*2) = √(4²*2)=4√2

Therefore,

→ (x)² - (1/x²)

→ (x + 1/x)(x - 1/x)

→ (6)(4√2)

→ 24√2

Answer:

4√2 & 24√2

Step-by-step explanation:

Square on both sides:

→ (x + 1/x)² = 6²

→ x² + 1/x² + 2(x*1/x) = 36

→ x² + 1/x² + 2(1) = 36

→ x² + 1/x² = 36 - 2 = 34

Subtract 2(x*1/x) from both sides:

→ x² + 1/x² - 2(x*1/x) = 34 - 2(x*1/x)

→ (x - 1/x)² = 34 - 2(1) = 32

→ x - 1/x = √32 = √(16*2) = √(4²*2)=4√2

Therefore,

→ (x)² - (1/x²)

→ (x + 1/x)(x - 1/x)

→ (6)(4√2)

→ 24√2