:(((((((help meeeeeeeee Question :(((((((help meeeeeeeee in progress 0 Môn Toán Philomena 5 years 2021-05-22T07:56:01+00:00 2021-05-22T07:56:01+00:00 2 Answers 34 views 0
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Giải thích các bước giải:
Bài 3:
Từ hệ suy ra:
$(x^2+y^2-2x-2y)+2(x+y-xy)=6+5\cdot 2$
$\to x^2+y^2-2xy=16$
$\to (x-y)^2=16$
$\to |x-y|=4$
Bài 4:
Ta có $\dfrac{x}{x^2+x+1}=\dfrac14$
$\to x^2+x+1=4x$
$\to x^2-3x+1=0$
Ta có:
$x^5-4x^3-3x+9$
$=(x^5-3x^4+x^3)+(3x^4-9x^3+3x^2)+(4x^3-12x^2+4x)+(9x^2-27x+9)+20x$
$=x^3(x^2-3x+1)+3x^2(x^2-3x+1)+4x(x^2-3x+1)+9(x^2-3x+1)+20x$
$=(x^3+3x^2+4x+9)(x^2-3x+1)+20$
$=20x$ vì $x^2-3x+1=0$
Ta có:
$x^4+3x^2+11$
$=(x^4-9x^2)+12x^2+11$
$=(x^2-3x)(x^2+3x)+12x^2+11$
$=-(x^2+3x)+12x^2+11$ vì $x^2-3x+1=0\to x^2-3x=-1$
$=11x^2-3x+11$
$=11(x^2+1)-3x$
$=11\cdot 3x-3x$ vfi $x^2-3x+1=0\to x^2+1=3x$
$=30x$
Ta có:
$P=\dfrac{x^5-4x^3-3x+9}{x^4+3x^2+11}=\dfrac{20x}{30x}=\dfrac23$