Question

已知x²－3x＝1,求：⑴x²＋1／x²的值；⑵x的4次方＋1／x的4次方的值

Answer 1

x²-3x=1;

x²-3x-1=0；

x-3-1/x=0;

x-1/x=3;

(1)x²+1/x²

=(x-1/x)²+2

=9+2

=11;

(2)x^4+1/x^4

=(x^2+1/x^2)^2-2

=11^2-2

=121-2

=119;

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