Question

if x + 1/x =1 find x^12 +x^9 +x^6 + x^3 + 1​

Answer 1

Step-by-step explanation:

$x + \frac{1}{x} = 1 \\ {x }^{2} + 1 = x \: \: \: \: ({x}^{2} - x + 1) = 0$

$now \: {x}^{3} + 1 = (x + 1)( {x}^{2} - x + 1) \\ (x + 1) \times 0 = 0$

${x}^{3} = - 1$

NOW,

${x}^{12} + {x}^{9} + {x}^{6} + {x}^{3} + 1 \\ = ({ {x}^{3} })^{4} + ( { {x}^{3} })^{3} + ({ {x}^{3} })^{2} + {x}^{3} + 1 \\ = ({ - 1})^{4} +( { - 1})^{3} + ( { - 1})^{2} + ( - 1) + 1 \\ = 1 - 1 + 1 - 1 + 1 = 1 \: \: answer$

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Answer 2

Step-by-step explanation:

if x+1/x = 1

x^3= -1

put the value of x^3 in eq we get

1-1+1-1+1=1