Question
If x2 - 7x + 1 = 0, then find the value
of: 3 + ( x 6 + x 4 + x 2 + 1)/ 7x 3Solution
Given, x2 - 7x + 1 = 0 Or, x2 + 1 = 7x - [I] x + 1/x = 7 - [II] = 3 + ( x 6 + x 4 + x 2 + 1)/ 7x 3 = 3 + { x 4( x 2 + 1) + ( x 2 + 1)}/( x 2 + 1) x 2 = 3 + ( x 2 + 1) + ( x 4 + 1)}/( x 2 + 1) x 2 = 3 + ( x 4 + 1)/ x 2 = 3 + x 2 + 1/ x 2 On squaring equation [II] x2 + 1/x2 + 2 = 49 Adding '1' both sides, we get x2 + 1/x2 + 3 = 50
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