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Given, k4 + (1/k4) = 47 we know, (k2 + (1/k2))2 = (k2)2 + (1/k2)2 + 2(k2)(1/k2) = k4 + (1/k4 ) + 2 = 47 + 2 = 49 = k2 + (1/k2) = 7 (k + 1/k)2 = k2 + (1/k2 ) + 2(k)(1/k) = (7 + 2) = 9 (k + (1/k)) = 3 we know that, k3 + (1/k3) = (k + (1/k)) × (k2 + (1/k2 ) - k × (1/k)) = 3(7 - 1) = 18
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