Question

if m-1/m =5 find: m2-1/m2

Answer 1

Correct Question :-

If m - 1/m = 5 , then find the value of m² - 1/m².

Answer :-

m² - 1/m² = 5√29

Solution :-

m - 1/m = 5----(1)

Find the value of m + 1/m

We know that

(x + y)² = (x - y)² + 4xy

Here

• m - 1/m = 5

By substituting the values

⇒ (m + 1/m)² = (m - 1/m)² + 4(m)(1/m)

⇒ (m + 1/m)² = (m - 1/m)² + 4

⇒ (m + 1/m)² = (5)² + 4

[Because m - 1/m = 5]

⇒ (m + 1/m)² = 25 + 4

⇒ (m + 1/m)² = 29

⇒ m + 1/m = √29 ----(2)

From (1) and (2)

⇒ (m + 1/m)(m - 1/m) = √29(5)

[Because (a + b)(a - b) = a² - b²]

⇒ (m)² - (1/m)² = 5√29

⇒ m² - 1²/m² = 5√29

⇒ m² - 1/m² = 5√29

Therefore the value of m² - 1/m² is 5√29.

Identities used :-

• (x + y)² = (x - y)² + 4xy

• (a + b)(a - b) = a² - b²