Question

If (X+1/X)=50/7 Then (X-1/X)=?

Answer 1

Answer :-

x - 1/x = 48/7

Solution :-

x + 1/x = 50/7

We know that

(a - b)² = (a + b)² - 4ab

Here

• a = x

• b = 1/x

By substituting the values

⇒ (x - 1/x)² = (x + 1/x)² - 4(x)(1/x)

⇒ (x - 1/x)² = (x + 1/x)² - 4

⇒ (x - 1/x)² = (50/7)² - 4

⇒ (x - 1/x)² = 50²/7² - 4

⇒ (x - 1/x)² = 2500/49 - 4

⇒ (x - 1/x)² = 2500/49 - 4/1

Taking LCM

⇒ (x - 1/x)² = 2500/49 - 4(49)/1(49)

⇒ (x - 1/x)² = 2500/49 - 196/49

⇒ (x - 1/x)² = (2500 - 196)/49

⇒ (x - 1/x)² = 2304/49

⇒ (x - 1/x)² = 48²/7²

⇒ (x - 1/x)² = (48/7)²

Cancelling squares on both sides

⇒ x - 1/x = 48/7

Identity used :-

• (a - b)² = (a + b)² - 4ab