Question

x+(1÷x)=3 then find x^2(1÷x^2)​

Answer 1

Answer:

X + 1/x = 3…(i)

We know ,

(X+1/x)^2 = x^2 + (1/x)^2 + 2(x * 1/x)

Substituting value from (i)

(3)^2 = x^2+(1/x)^2+2

= 9–2 = x^2+(1/x)^2

X^2 + (1/x)^2 = 7.

Answer 2

Answer:

The value of x² + ( 1 / x² ) is 7.

Step-by-step-explanation:

We have given that,

x + ( 1 / x ) = 3

We have to find the value of

x² + ( 1 / x² ).

Now,

x + ( 1 / x ) = 3

By squaring both sides, we get,

[ x + ( 1 / x ) ]² = 3²

We know that,

( a + b )² = a² + 2ab + b²

⇒ x² + ( 1 / x² ) + 2 * x * 1 / x = 9

⇒ x² + ( 1 / x² ) + 2 = 9

⇒ x² + ( 1 / x² ) = 9 - 2

⇒ x² + ( 1 / x² ) = 7

∴ The value of x² + ( 1 / x² ) is 7.

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Additional Information:

Some Algebraic Identities:

1. ( a + b )² = a² + 2ab + b²

2. ( a - b )² = a² - 2ab + b²

3. a² - b² = ( a + b ) ( a - b )

4. ( a + b )³ = a³ + 3a²b + 3ab² + b³

5. ( a - b )³ = a³ - 3a²b + 3ab² - b³

6. a³ + b³ = ( a + b ) ( a² + b² - ab )

7. a³ - b³ = ( a - b ) ( a² + b² + ab )

8. ( a + b + c )² = a² + b² + c² + 2ab + 2bc + 2ac

9. ( a + b + c )³ = a³ + b³ + c³ + 3 ( a + b ) ( b + c ) ( c + a )