Question

If a^2+1/a^2 =7 then find a-1/a

Answer 1

Solution:

Given That:

→ a² + 1/a² = 7

Subtracting 2 from both sides, we get:

→ a² + 1/a² - 2 = 5

Can be written as:

→ (a)² + (1/a)² - 2 × (a) × (1/a) = 5

Using identity (a - b)² = a² - 2ab + b², we get:

→ (a - 1/a)² = 5

→ a - 1/a = √5

★ Which is our required answer.

Answer:

• The value of a - 1/a is √5

Learn More:

Algebraic Identities.

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• (a + b)² + (a - b)² = 2(a² + b²)
• (a + b)² - (a - b)² = 4ab
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab
• (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac