7. If x² + 1/x²= 83, find the value of x - 1/x²
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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.
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Question:-
7. If
Given:-
To Find:-
Solution:-
Answer:-
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