a) \(2\left(3x-1\right)-\left(5+3x\right)=3\left(2x-1\right)\)

\(\Leftrightarrow6x-2-5-3x=6x-3\)

\(\Leftrightarrow6x-3x-6x=-3+2+5\)

\(\Leftrightarrow-3x=4\)

\(\Leftrightarrow x=-\frac{4}{3}\)

b) \(3\left(x-\frac{1}{2}\right)+4\left(\frac{x}{3}-\frac{1}{3}\right)=\frac{x}{4}\)

\(\Leftrightarrow3x-\frac{3}{2}+\frac{4}{3}x-\frac{4}{3}=\frac{x}{4}\)

\(\Leftrightarrow3x+\frac{4}{3}x-\frac{x}{4}=\frac{3}{2}+\frac{4}{3}\)

\(\Leftrightarrow\frac{49}{12}x=\frac{17}{6}\)

\(\Leftrightarrow x=\frac{34}{49}\)

c) \(\frac{1}{5}\left(x-\frac{1}{3}\right)-4\left(\frac{x}{5}-\frac{1}{2}\right)=x\)

\(\Leftrightarrow\frac{1}{5}x-\frac{1}{15}-\frac{4}{5}x+2=x\)

\(\Leftrightarrow\frac{1}{5}x-\frac{4}{5}x-x=\frac{1}{15}-2\)

\(\Leftrightarrow-\frac{8}{5}x=-\frac{29}{15}\)

\(\Leftrightarrow x=\frac{29}{24}\)

a,Bạn xét 3 th

th1: x>=-1

th2: 1>x>-1

th3:x<=1

rồi trong từng th bạn bỏ dấu gttd và giải

b, \(\frac{x^2}{3}+\frac{48}{x^2}=10\left(\frac{x}{3}-\frac{4}{x}\right)\)

tương đương \(x^2+\frac{144}{x^2}=10\left(x-\frac{12}{x}\right)\)(nhân cả 2 vế với 3)

tương đương \(\left(x-\frac{12}{x}\right)^2+24-10\left(x-\frac{12}{x}\right)\)=0

đặt (x-12/x)=a

khi đó a^2-10a+24=0

giải a rồi tìm x thôi 

c, đặt \(\sqrt[3]{x}\)=a

khi đó ta có 2a^2-5a=3

giải a rồi tìm x thôi

Chúc bạn học tốt!

a/ \(x=\dfrac{-5}{12}\)

b/ \(x\approx-1,9526\)

c/ \(x=\dfrac{21-i\sqrt{199}}{10}\)

d/ \(x=\dfrac{-20}{13}\)

a) (x-2)³+6(x+1)²-x³+12=0

⇒ x³-6x²+12x-8+6(x²+2x+1)-x³+12=0

⇒ x³-6x²+12x-8+6x²+12x+6-x³+12=0

⇒ 24x+10=0

⇒ 24x=-10

⇒ x=-5/12

a.

PT \(\Leftrightarrow x^3-6x^2+12x-8+6(x^2+2x+1)-x^3+12=0\)

\(\Leftrightarrow x^3-6x^2+12x-8+6x^2+12x+6-x^3+12=0\)

\(\Leftrightarrow 24x+10=0\Leftrightarrow x=\frac{-5}{12}\)

b. Bạn xem lại đề, nghiệm khá xấu không phù hợp với mức độ tổng thể của bài.

c.

PT $\Leftrightarrow (4x^2+12x+9)+(x^2-1)=5(x^2+4x+4)+(x^2-4x-5)+9(x^2+6x+9)$
$\Leftrightarrow 10x^2+42x+64=0$

$\Leftrightarrow x^2+(3x+7)^2=-15< 0$ (vô lý) 

Do đó pt vô nghiệm.

d.

PT $\Leftrightarrow (1-6x+9x^2)-(9x^2-17x-2)=(9x^2-16)-9(x^2+6x+9)$

$\Leftrightarrow 11x+3=-54x-97$

$\Leftrightarrow 65x=-100$

$\Leftrightarrow x=\frac{-20}{13}$

a)\(\left(x-2\right)\left(5-x\right)=7x-\left(x-1\right)\left(3-2x\right)\Leftrightarrow5x-x^2-10+2x=7x-3x+2x^2+3-2x\Leftrightarrow-3x^2+5x-13=0\)\(\Delta=b^2-4ac=25-4.\left(-3\right).\left(-13\right)=-131< 0\)

\(\Rightarrow\)phương trình vô nghiệm

Dùng liên hợp.

pt <=> \(\left(x-\sqrt{2}\right)\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)\left(1+\sqrt{3}\right)\)

\(-3\left(x-1\right)\left(x-\sqrt{3}\right)\left(\sqrt{2}+1\right)\left(\sqrt{2}+\sqrt{3}\right)\)

\(+2\left(x-1\right)\left(x-\sqrt{2}\right)\left(\sqrt{3}+1\right)\left(\sqrt{3}+\sqrt{2}\right)=3x-1\)

<=> \(\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)\left[\left(x-\sqrt{2}\right)\left(1+\sqrt{3}\right)-\left(x-1\right)\left(\sqrt{2}+\sqrt{3}\right)\right]\)

\(-2\left(x-1\right)\left(\sqrt{3}+\sqrt{2}\right)\left[\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)-\left(x-\sqrt{2}\right)\left(1+\sqrt{3}\right)\right]\)

\(=3x-1\)

<=> \(\left(x-\sqrt{3}\right)\left(1+\sqrt{2}\right)\left(x+\sqrt{3}\right)\left(1-\sqrt{2}\right)\)

\(-2\left(x-1\right)\left(\sqrt{3}+\sqrt{2}\right)\left(x+1\right)\left(\sqrt{2}-\sqrt{3}\right)=3x-1\)

<=> \(3-x^2-2\left(1-x^2\right)=3x-1\)

<=> \(x^2-3x+2=0\) phương trình bậc 2.

Em làm tiếp nhé!

Bài 5 :

a, Ta có : \(\frac{\left(2x+1\right)^2}{5}-\frac{\left(x-1\right)^2}{3}=\frac{7x^2-14x-5}{15}\)

=> \(\frac{3\left(2x+1\right)^2}{15}-\frac{5\left(x-1\right)^2}{15}=\frac{7x^2-14x-5}{15}\)

=> \(3\left(2x+1\right)^2-5\left(x-1\right)^2=7x^2-14x-5\)

=> \(12x^2+12x+3-5x^2+10x-5-7x^2+14x+5=0\)

=> \(36x+3=0\)

=> \(x=-\frac{1}{12}\)

Vậy phương trình trên có nghiệm là \(S=\left\{-\frac{1}{12}\right\}\)

b, Ta có : \(\frac{7x-1}{6}+2x=\frac{16-x}{5}\)

=> \(\frac{5\left(7x-1\right)}{30}+\frac{60x}{30}=\frac{6\left(16-x\right)}{30}\)

=> \(5\left(7x-1\right)+60x=6\left(16-x\right)\)

=> \(35x-5+60x-96+6x=0\)

=> \(101x-101=0\)

=> \(x=1\)

Vậy phương trình trên có tạp nghiệm là \(S=\left\{1\right\}\)

c, Ta có : \(\frac{\left(x-2\right)^2}{3}-\frac{\left(2x-3\right)\left(2x+3\right)}{8}+\frac{\left(x-4\right)^2}{6}=0\)

=> \(\frac{8\left(x-2\right)^2}{24}-\frac{3\left(2x-3\right)\left(2x+3\right)}{24}+\frac{4\left(x-4\right)^2}{24}=0\)

=> \(8\left(x-2\right)^2-3\left(2x-3\right)\left(2x+3\right)+4\left(x-4\right)^2=0\)

=> \(8\left(x^2-4x+4\right)-3\left(4x^2-9\right)+4\left(x^2-8x+16\right)=0\)

=> \(8x^2-32x+32-12x^2+27+4x^2-32x+64=0\)

=> \(-64x+123=0\)

=> \(x=\frac{123}{64}\)

Vậy phương trình có nghiệm là \(S=\left\{\frac{123}{64}\right\}\)

a) \(x-2=\left(x-2\right)^2\)

\(\left(x-2\right)^2-\left(x-2\right)=0\)

\(\left(x-2\right)\left(x-2-1\right)=0\)

\(\left(x-2\right)\left(x-3\right)=0\)

\(\Rightarrow x-2=0\) hoặc \(x-3=0\)

*) \(x-2=0\)

\(x=2\)

*) \(x-3=0\)

\(x=3\)

Vậy \(x=2;x=3\)

b) \(x+5=2\left(x+5\right)^2\)

\(2\left(x+5\right)^2-\left(x+5\right)=0\)

\(\left(x+5\right)\left[2\left(x+5\right)-1\right]=0\)

\(\left(x+5\right)\left(2x+10-1\right)=0\)

\(\left(x+5\right)\left(2x+9\right)=0\)

\(\Rightarrow x+5=0\) hoặc \(2x+9=0\)

*) \(x+5=0\)

\(x=-5\)

*) \(2x+9=0\)

\(2x=-9\)

\(x=-\dfrac{9}{2}\)

Vậy \(x=-5;x=-\dfrac{9}{2}\)

c) \(\left(x^2+1\right)\left(2x-1\right)+2x=1\)

\(\left(x^2+1\right)\left(2x-1\right)+2x-1=0\)

\(\left(x^2+1\right)\left(2x-1\right)+\left(2x-1\right)=0\)

\(\left(2x-1\right)\left(x^2+1+1\right)=0\)

\(\left(2x-1\right)\left(x^2+2\right)=0\)

\(\Rightarrow2x-1=0\) hoặc \(x^2+2=0\)

*) \(2x-1=0\)

\(2x=1\)

\(x=\dfrac{1}{2}\)

*) \(x^2+2=0\) 

\(x^2=-2\) (vô lí)

Vậy \(x=\dfrac{1}{2}\)

d) Sửa đề:

\(\left(x^2+3\right)\left(x+1\right)+x=-1\)

\(\left(x^2+3\right)\left(x+1\right)+\left(x+1\right)=0\)

\(\left(x+1\right)\left(x^2+3+1\right)=0\)

\(\left(x+1\right)\left(x^2+4\right)=0\)

\(\Rightarrow x+1=0\) hoặc \(x^2+4=0\)

*) \(x+1=0\)

\(x=-1\)

*) \(x^2+4=0\)

\(x^2=-4\) (vô lí)

Vậy \(x=-1\)

Câu hỏi của Phương Boice - Toán lớp 8 - Học toán với OnlineMath