Question

if z²+1/z²=18 find z-1/z​

Answer 1

Answer:

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Answer 2

Required Answer:-

Given:

• z² + 1/z² = 18

To Find:

• z - 1/z = ?

Answer:

• z - 1/z = ±4

Solution:

We have,

➡ z² + 1/z² = 18

Subtracting 2 from both sides,

➡ (z)² + (1/z)² - 2 × z × 1/z = 18 - 2 × x × 1/x

Using identity, (x - y)² = x² - 2xy + y², we get,

➡ (z - 1/z)² = 18 - 2

➡ z - 1/z = √16

➡ z - 1/z = ±4

★ Hence, the value of z - 1/z is ±4

More Identities:

• (a + b)² = a² + 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³