Math, asked by shivameltctp, 4 days ago

7. If x² + 1/x²= 83, find the value of x - 1/x²​

Answers

Answered by amansharma264
2

EXPLANATION.

⇒ (x² + 1/x²) = 83.

As we know that,

Formula of :

⇒ (a - b)² = a² + b² - 2ab.

Using this formula in the equation, we get.

⇒ (x - 1/x)² = (x)² + (1/x)² - 2(x)(1/x).

⇒ (x - 1/x)² = x² + 1/x² - 2.

Put the values of (x² + 1/x²) = 83 in the equation, we get.

⇒ (x - 1/x)² = 83 - 2.

⇒ (x - 1/x)² = 81.

⇒ (x - 1/x) = √81.

(x - 1/x) = ± 9.

                                                                                                                     

MORE INFORMATION.

(1) (a + b)² = a² + b² + 2ab.

(2) (a - b)² = a² + b² - 2ab.

(3) (a² - b²) = (a - b)(a + b).

(4) (a² + b²) = (a + b)² - 2ab.

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

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

(7) (a + b)³ = a³ + 3a²b + 3ab² + b³.

(8) (a - b)³ = a³ - 3a²b + 3ab² - b³.

Answered by XxitzZBrainlyStarxX
5

Question:-

7. If

 \sf \large x {}^{2}  +  \frac{1}{x {}^{2} }  = 83. \:  Find \: the \: value \: of \: x -  \frac{1}{x {}^{2} } .

Given:-

 \sf \large x {}^{2}  +  \frac{1}{x {}^{2} }  = 83.

To Find:-

 \sf \large value \: of \: x -  \frac{1}{x {}^{2} }.

Solution:-

 \sf \large x {}^{2}  +  \frac{1}{x {}^{2} }  = 83

 \sf \large ⇒x {}^{2}  +  \frac{1}{x {}^{2} }  - 2 = 83 - 2

 \sf \large⇒(x {}^{2} ) + ( \frac{1}{x {}^{} } ) {}^{2}  - 2(x)( \frac{1}{x} ) = 81

 \sf \large⇒(x -  \frac{1}{x} ) {}^{2}  = 81 \:  \:  \:  \:  \:  \:  \:  \:  \bigg[ \because a {}^{2} + b {}^{2}  - 2ab = (a - b) {}^{2}  \bigg ]

 \sf \large⇒x -  \frac{1}{x  }  =  ±9

Answer:-

 \sf \large \color{red}x -  \frac{1}{x  }  = ±9.

Hope you have satisfied.

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