Register Now

Login

Lost Password

Lost your password? Please enter your email address. You will receive a link and will create a new password via email.

222-9+11+12:2*14+14 = ? ( )

Toán Lớp 8: Giari PT (2x^2 – x + 2)(2x^2 – 3x + 2) – 8x^2 = 0

Tháng Sáu 13, 2022 Toán học 2 Comments 0 views

Toán Lớp 8: Giari PT
(2x^2 – x + 2)(2x^2 – 3x + 2) – 8x^2 = 0

Comments ( 2 )

  1. giahan44
    giahan44
    13 Tháng Sáu, 2022 at 2:32 sáng
    Reply
    Ta có :
    (2x^2 -x+2)(2x^2 -3x+2) -8x^2 =0
    <=>4x^4 -8x^3 +11x^2 -8x+4 -8x^2 =0
    <=> 4x^4 -8x^3 +3x^2 -8x +4 =0   
    <=>4x^4 – 8x^3 +3x^2 – 6x -2x+4=0
    <=> 4x^3(x-2) + 3x(x-2) – 2(x-2) =0
    <=> (4x^3 +3x-2)(x-2) =0  
     <=> (4x^3 – 2x^2 +2x^2 – x + 4x -2)(x-2) =0
    <=> [ 2x^2(2x-1) + x(2x-1) + 2(2x-1)](x-2) =0
    <=> (2x^2 +x+2)(2x-1)(x-2) =0    
    $\\$
    Vì : 
    $\\$
    2x^2+x+2=2(x^2+1/2x +1) = 2(x^2+2 . x . 1/4 +1/16 +15/16)=2(x+1/4)^2+15/8 \ge 15/8 > 0 AAx \in RR 
    Nên : \(\left[ \begin{array}{l}2x-1 =0\\x-2 =0\end{array} \right.\) 
    $\\$
    <=> \(\left[ \begin{array}{l}2x =1\\x=2\end{array} \right.\) 
    $\\$
    <=> \(\left[ \begin{array}{l}x=\dfrac{1}{2}\\x=2\end{array} \right.\) 
    $\\$
    Vậy S = {1/2 ;2}

  2. thanhbinh2k5
    thanhbinh2k5
    13 Tháng Sáu, 2022 at 2:32 sáng
    Reply
    $\\$
    Đặt 2x^2-3x+2=t
    <=>2x^2-3x+2+2x=t+2x
    <=>2x^2 – x +2=t+2x
    Khi đó pt trở thành :
    (t+2x)t-8x^2 = 0
    <=> t^2+2xt – 8x^2=0
    <=>t^2+4xt – 2xt – 8x^2 = 0
    <=>t(t+4x) – 2x (t+4x)=0
    <=>(t-2x)(t+4x)=0
    <=> (2x^2-3x+2-2x)(2x^2-3x+2+4x)=0
    <=> (2x^2  -5x+2) (2x^2 +x+2)=0
    Do 2x^2+x+2=2(x^2+1/2 x +1) = 2(x^2+2 . x . 1/4 +1/16 +15/16)=2(x+1/4)^2+15/8\ge 15/8 > 0∀x
    <=>2x^2-5x+2=0
    <=>2x^2 – x – 4x+2=0
    <=>x(2x-1)-2(2x-1)=0
    <=> (2x-1)(x-2)=0
    <=>2x-1=0 hoặc x-2=0
    <=>x=1/2 hoặc x=2
    Vậy pt có tập nghiệm : S={1/2;2}

Leave a reply

222-9+11+12:2*14+14 = ? ( )

Dương

About Dương