Question

if X+1/x=5 find x-1/x

Answer 1

x²+1/x²= (x+1/x)² - 2× x × 1/x

        = 25 - 2 = 23

x²+1/x² = ( x- 1/x)² + 2 × x × 1/x

∴ x-1/x = √21

OK

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Answer 2

Answer :-

x - 1/x = √21

Explanation :-

Given :-

x + 1/x = 5

To find :-

x - 1/x

Solution :-

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 = (5)² - 4

[Since x + 1/x = 5]

⇒ (x - 1/x)² = 25 - 4

⇒ (x - 1/x)² = 21

⇒ x - 1/x = √21

Therefore the value of x - 1/x is √21.

Identity used :-

• (a - b)² = (a + b)² - 4ab