Toán Lớp 8: x^4-2x^3+10x^2-20x=0 15-2x-x^2=0

Question

Toán Lớp 8:  x^4-2x^3+10x^2-20x=0 15-2x-x^2=0

tuyetnhungthu · Answer

x ^ 4 - 2 x ^ 3 + 10 x ^ 2 - 20 x = 0   => x ( x ^ 3 - 2 x ^ 2 + 10 x- 20 )   => x ( x ^ 2 ( x - 2 ) + 10 ( x - 2 ) = 0   => x ( x - 2 )  (x ^ 2 + 10 ) = 0   =>x = 0 hoặc  x = 2           15 - 2 x - 2 x = 0                  =0 1 5      &minus; 2 x &minus; x 2 = 0              &hArr;     16     &minus;      ( x 2 + 2 x + 1     )      =     0      &hArr; 16 &minus; [ x 2 + 2 x + 1) = 0              &hArr; 16     &minus;        (      x     +     1      ) 2 = 0         &hArr; 16 &minus; ( x + 1 )  2 = 16                 &hArr;      [               x     +     1     = 4 x + 1           =     &minus;     4              &hArr;      [ x = 3 x           =     &minus;     5               &hArr; [ x + 1 = 4 x + 1 = &minus; 4 &hArr; [ x = 3 x = &minus; 5        vậy         [ x = 3 x           &minus;     5

hoaiphuong85 · Answer

Giải đáp: a, S={0;2} b, S={-5;3} Lời giải và giải thích chi tiết: a, x⁴ -2x³ +10x² -20x=0 <=> x³(x -2)+10x(x-2)=0 <=> (x³+10x)(x-2)=0 <=> x(x²+10)(x-2)=0 <=> ( left[ begin{array}{l}x=0 x²+10=0 x-2=0 end{array} right. ) <=> ( left[ begin{array}{l}x=0 x²=-10 (vô lí) x=2 end{array} right. ) Vậy S={0;2} b, 15-2x -x² =0 <=> x² +2x -15=0 <=> x² +5x -3x -15=0 <=> x(x+5) -3(x+5)=0 <=> (x+5)(x-3)=0 <=> ( left[ begin{array}{l}x+5=0 x-3=0 end{array} right. ) <=> ( left[ begin{array}{l}x=-5 x=3 end{array} right. ) Vậy S={-5;3}