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If a+1/a=2, prove that a^2+1/a^2=a^4+1/a^4=a^3+1/a^3 |
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Answer» Step-by-step EXPLANATION: a + 1/a = 2 (a+1/a)^2 = (2)^2 a^2 + 2 + 1/a^2 = 4 a^2 + 1/a^2 = 2 a^2 + 1/a^2 = a + 1/a = 2 (a^2 + 1/a^2) (a + 1/a) = 2x2 a^3 + a + 1/a + 1/a^3 =4 a^3 + 2 + 1/a^3 =4 a^3 + 1/a^3 = 2 (a^2 + 1/a^2)(a^2 + 1/a^2) = 2x2 a^4 + 2 + 1/a^4 = 4 a^4 + 1/a^4 = 2 a + 1/a = 2 = a^2 + 1/a^2 = a^3 + 1/a^3 = a^4 + 1/a^4 (PROVED) |
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