Question

a2+1/a2=18 find (a-1/a)

Answer 1

a^2 + 1/a^2 = 18 

Add -2(a × 1/a) on both sides,



a^2 + 1/a^2 - 2(a × 1/a) = 18 - 2(a × 1/a)

(a  - 1/a)^2 = 18 - 2 

(a - 1/a)^2 = 16 

a - 1/a       = 4 




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Answer 2

Correct Question :-

If a² + 1/a² = 18, then find the value of a - 1/a.

Answer :-

a - 1/a = 4

Solution :-

a² + 1/a² = 18

Subtract 2 on both sides

a² + 1/a² - 2 = 18 - 2

⇒ a² + 1/a² - 2 = 16

⇒ a² + 1²/a² - 2 = 16

It can be written as

⇒ (a)² + (1/a)² - 2(a)(1/a) = 16

We know that

(x - y)² = x² + y² - 2xy

Here x = a, y = 1/a

By substituting the values

⇒ (a - 1/a)² = 16

⇒ a - 1/a = √16

⇒ a - 1/a = 4

Therefore the value of a - 1/a is 4.

Identity used :-

• (x - y)² = x² + y² - 2xy