已知y²+3y-1=0求y²+1/y²的值

已知y²+3y-1=0求y²+1/y²的值
已知y²+3y-1=0求y²+1/y²的值

已知y²+3y-1=0求y²+1/y²的值
y²+3y-1=0
等式两边同除以y
y +3 -1/y=0
y - 1/y=-3
y²+ 1/y²
=(y- 1/y)² +2
=(-3)²+2
=11

已知y^2+3y-1=0，则y^2+3y+9/4=13/4 得(y+3/2)^2=13/4 解得y=(√13-3)/2或y=(-√13-3)/2

则y^2+1/y^2=[(√13-3)/2]^2+1/[(√13-3)/2]^2=(22-6√13)/4-4/(22-6√13)=(22-6√13)/4-4(22+6√13)/16=(22-6√13)/4-(22+6√13)/4=-3...

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已知y^2+3y-1=0，则y^2+3y+9/4=13/4 得(y+3/2)^2=13/4 解得y=(√13-3)/2或y=(-√13-3)/2

则y^2+1/y^2=[(√13-3)/2]^2+1/[(√13-3)/2]^2=(22-6√13)/4-4/(22-6√13)=(22-6√13)/4-4(22+6√13)/16=(22-6√13)/4-(22+6√13)/4=-3√13
或者y^2+1/y^2=[(-√13-3)/2]^2+1/[(-√13-3)/2]^2=(22+6√13)/4-4/(22+6√13)=(22+6√13)/4-4(22-6√13)/16=(22+6√13)/4-(22-6√13)/4=3√13
因此y^2+1/y^2=-3√13或3√13

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