Toán Lớp 8: tìm x,biết: a,(x-2)(x+2)-(x-3)^2=9 b,(x-1)(x^2+1)-(x+1)(x^2-x+1)=x(2-x) c,(x-3)(x^2+3x+9)+x(x+2)(2-x)=1 d,(x+1)^3-(x-1)^3-6(x-1)^2=-19

Question

Toán Lớp 8:  tìm x,biết: a,(x-2)(x+2)-(x-3)^2=9 b,(x-1)(x^2+1)-(x+1)(x^2-x+1)=x(2-x) c,(x-3)(x^2+3x+9)+x(x+2)(2-x)=1 d,(x+1)^3-(x-1)^3-6(x-1)^2=-19

quynhthanhnghi · Answer

Lời giải:     a)   (x-2)(x+2)-(x-3)^(2)=9   &hArr;x^(2)-4-(x^(2)-6x+9)=9   &hArr;x^(2)-4-x^(2)+6x-9=9   &hArr;(x^(2)-x^2)+6x=9+9+4   &hArr;6x=22   &hArr;x=22/6=11/3   Vậy x=11/3   b)   (x-1)(x^(2)+1)-(x+1)(x^(2)-x+1)=x(2-x)   &hArr;x^(3)+x-x^(2)-1-(x^(3)+1)=2x-x^2   &hArr;x^(3)-x^(2)+x-1-x^(3)-1-2x+x^2=0   &hArr;(x^(3)-x^3)+(-x^(2)+x^2)+(x-2x)-2=0   &hArr;-x-2=0   &hArr;x=-2   Vậy x=-2   c)   (x-3)(x^(2)+3x+9)+x(x+2)(2-x)=1   &hArr;(x^(3)-27)+x(2+x)(2-x)=1   &hArr;x^(3)-27+x(4-x^2)=1   &hArr;x^(3)-27+4x-x^3=1   &hArr;x^(3)-x^(3)+4x=1+27   &hArr;4x=28   &hArr;x=7   Vậy x=7   d)   (x+1)^(3)-(x-1)^(2)-6(x-1)^2=-19   &hArr;x^(3)+3x^(2)+3x+1-(x^(3)-3x^(2)+3x-1)-6(x^(2)-2x+1)=-19   &hArr;x^(3)+3x^(2)+3x+1-x^(3)+3x^(2)-3x+1-6x^(2)+12x-6=-19   &hArr;(x^(3)-x^3)+(3x^(2)+3x^2-6x^2)+(3x-3x+12x)+(1+1-6+19)=0   &hArr;12x+15=0   &hArr;12x=-15   &hArr;x=-5/4   ậy x=-5/4

thuminhthong · Answer

Lời giải và giải thích chi tiết: a, (x-2)(x+2)-(x-3)^2=9 <=> x^2-4-(x^2-6x+9)=9 <=> x^2-4-x^2+6x-9=9 <=> (x^2-x^2)+6x=9+9+4 <=> 6x=22 <=> x=11/3 Vậy x=11/3 b, (x-1)(x^2+1)-(x+1)(x^2-x+1)=x(2-x) <=> x^3+x-x^2-1-(x^3+1)=2x-x^2 <=> x^3-x^2+x-1-x^3-1+x^2-2x=0 <=> (x^3-x^3)+(x^2-x^2)+(x-2x)=1+1 <=> -x=2 <=> x=-2 Vậy x=-2 c, (x-3)(x^2+3x+9)+x(x+2)(2-x)=1 <=> x^3-27-x(x^2-4)=1 <=> x^3-27-x^3+4x=1 <=> (x^3-x^3)+4x=1+27 <=> 4x=28 <=> x=7 Vậy x=7 d, (x+1)^3-(x-1)^3-6(x-1)^2=-19 <=> x^3+3x^2+3x+1-(x^3-3x^2+3x-1)-6(x^2-2x+1)=-19 <=> x^3+3x^2+3x+1-x^3+3x^2-3x+1-6x^2+12x-6=-19 <=> (x^3-x^3)+(3x^2+3x^2-6x^2)+(3x-3x+12x)=-19+6-1-1 <=> 12x=-15 <=> x=-5/4 Vậy x=-5/4