Question
If x4 + x - 4 = 47 then find the
value of (x + x-1).Solution
x4 + x - 4 = 47 x4 + 1/x 4 = 47 Add 2 both sides x4 + 1/x 4 + 2 = 49 The above expression is of the form a2 + b2 + 2ab = (a + b)2 where a = x and b = 1/x Then the above expression becomes (x2 + 1/x2)2 =72 Taking square root on both sides (x2 + 1/x2) = 7 Again adding 2 both sides (x2 + 1/x2 + 2) = 9 (x + 1/x)2 = 32 Taking square root on both sides (x + 1/x) = 3
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