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If x = 1/x-5 x ≠ 5, find : x²-1/x² |
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Answer» Here you go mateStep-by-step explanation: x = 1 / ( x - 5 ) x -5 = 1 / x [since x is not equal to zero] LET x - 1 / x = 5 be (1)Squaring both sides ( x - 1 / x ) ^ 2 = 25 [ x^2 – 2x( 1/x ) + 1 ] / (x^2) = 25 x^2 – 2 + 1 / (x^2) = 25 x^2 + 1 / (x^2) = 25 + 2 = 27Adding 2 to both sides we have x^2 + 2 + 1 / (x^2) = 29 x^2 + 2x( 1/x ) + 1/( x^2 ) = 29 ( x + 1 / x )^2 = 29 Let x + 1 / x = (29) ^ ( 1/2 ) be (2)Multiplying (1) and (2) we have x^2–1/x^2=+-5×(29)^(1/2)Hope it helps.Please mark me a the BRAINLIEST. |
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