viết lại đề đi, chả hiểu j

Câu b ak

a)\(\dfrac{3x+2}{3x-2}-\dfrac{6}{2+3x}=\dfrac{9x^2}{9x^2-4}\left(ĐKXĐ:x\ne\pm\dfrac{2}{3}\right)\)

\(\Leftrightarrow\dfrac{3x+2}{3x-2}-\dfrac{6}{3x+2}=\dfrac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\)

\(\Leftrightarrow\dfrac{\left(3x+2\right)^2-6\left(3x-2\right)}{\left(3x-2\right)\left(3x+2\right)}=\dfrac{9x^2}{\left(3x-2\right)\left(3x+2\right)}\)

\(\Rightarrow9x^2+12x+4-18x+12=9x^2\)

\(\Leftrightarrow9x^2-6x+16-9x^2=0\)

\(\Leftrightarrow-6x=-16\)

\(\Leftrightarrow x=\dfrac{8}{3}\) (thỏa mãn ĐKXĐ)

Vậy .................

b) \(\dfrac{5-x}{4x^2-8x}+\dfrac{7}{8x}=\dfrac{x-1}{2x\left(x-2\right)}+\dfrac{1}{8x-16}\left(ĐKXĐ:x\ne0;x\ne2\right)\)

\(\Leftrightarrow\dfrac{5-x}{4x\left(x-2\right)}+\dfrac{7}{8x}=\dfrac{x-1}{2x\left(x-2\right)}+\dfrac{1}{8\left(x-2\right)}\)

\(\Leftrightarrow\dfrac{2\left(5-x\right)+7\left(x-2\right)}{8x\left(x-2\right)}=\dfrac{4\left(x-1\right)+x}{8x\left(x-2\right)}\)

\(\Rightarrow10-2x+7x-14=4x-4+x\)

\(\Leftrightarrow5x-4=5x-4\)

\(\Leftrightarrow0x=0\) (vô số nghiệm)

Vậy \(S=R\backslash\left\{0;2\right\}\)

Bài 1:

\(f\left(x\right)=-x^{15}+8x^{14}-8x^{13}+...-8x-5\)

Ta xét \(x=7\Leftrightarrow x+1=8\)

Khi đó :

\(f\left(7\right)=-x^{15}+x^{14}\left(x+1\right)-x^{13}\left(x+1\right)+...-x\left(x+1\right)-5\)

\(f\left(7\right)=-x^{15}+x^{15}+x^{14}-x^{14}-x^{13}+...-x^2-x-5\)

\(f\left(7\right)=-x-5\)

\(f\left(7\right)=-7-5\)

\(f\left(7\right)=-12\)

Vậy...

a,\(x\left(8x-2\right)-8x^2+12=0\)

\(\Leftrightarrow8x^2-2x-8x^2+12=0\)

\(\Leftrightarrow-2x+12=0\)

\(\Leftrightarrow-2x=-12\)

\(\Leftrightarrow x=6\)

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

\(\Leftrightarrow4x^2-5x-\left(4x^2+4x+1\right)=0\)

\(\Leftrightarrow4x^2-5x-4x^2-4x-1=0\)

\(\Leftrightarrow-9x-1=0\)

\(\Leftrightarrow-9x=1\)

\(\Leftrightarrow x=\frac{-1}{9}\)

A:x(8x -2) -8x²+12=0

8x²-2x-8x²+12=0

-2x+12=0

-2x=-12

x=6

Vậy......

b:x(4x-5)-(2x+1)²=0

4x²-5x-4x²-4x-1=0

-9x=1

x=-1/9

Vậy....

Ta có : x = 7 ⇒ x + 1 = 8

Thay x + 1 = 8 vào A , ta được :

A = x¹⁵ - ( x + 1)x¹⁴ + ( x + 1)x¹³ - ( x + 1)x¹² +....- ( x + 1)x² + ( x + 1)x - 5

A = x¹⁵ - x¹⁵ - x¹⁴ + x¹⁴ + x¹³ - x¹³ - x¹² +....- x³ - x² + x² + x - 5

A = x - 5 = 7 - 5 = 2

\(a.17+8x=10-6x\\\Leftrightarrow 8x+6x=-17+10\\\Leftrightarrow 2x=-7\\ \Leftrightarrow x=-\frac{7}{2}\)

Vậy nghiệm của phương trình trên là \(-\frac{7}{2}\)

\(b.3\left(x+5\right)+7=19-5\left(x-2\right)\\\Leftrightarrow 3x+15+7=19-5x+10\\ \Leftrightarrow3x+5x=-15-7+19+10\\ \Leftrightarrow8x=7\\\Leftrightarrow x=\frac{7}{8}\)

Vậy nghiệm của phương trình trên là \(\frac{7}{8}\)

\(c.3x-4\left(x+2\right)\left(x+3\right)=14-4\left(x^2-3x\right)\\ \Leftrightarrow3x-4\left(x^2+5x+6\right)=14-4x^2+12x\\ \Leftrightarrow4x^2-4x^2+3x-5x-12x=24+14\\ \Leftrightarrow-14x=38\\ \Leftrightarrow x=-\frac{19}{7}\)

Vậy nghiệm của phương trình trên là \(-\frac{19}{7}\)

\(d.x+\frac{3}{4}+3x+2=\frac{x}{3}-3x-\frac{2}{6}\\ \Leftrightarrow\frac{12x}{12}+\frac{9}{12}+\frac{36x}{12}+\frac{24}{12}=\frac{4x}{12}-\frac{36x}{12}-\frac{4}{12}\\ \Leftrightarrow12x+9+36x+24=4x-36x-4\\ \Leftrightarrow12x+36x+36x-4x=-24-9-4\\ \Leftrightarrow80x=-37\\ \Leftrightarrow x=-\frac{37}{80}\)

`4|8x-3|+5|3-2x|=18`

`<=>4|8x-3|+5|2x-3|=18`

Nếu `x>=3/2=>|8x-3|=8x-3,|2x-3|=2x-3`

`pt<=>4(8x-3)+5(2x-3)=18`

`<=>32x-12+10x-15=18`

`<=>42x=27+18=45`

`<=>x=45/42(l)`

Nếu `x<=3/8=>|8x-3|=3-8x,|2x-3|=3-2x`

`pt<=>4(3-8x)+5(3-2x)=18`

`<=>12-32x+15-10x=18`

`<=>27-42x=18`

`<=>9=42x`

`<=>x=3/14(tm)`

Nếu `3/9<=x<=3/2=>|8x-3|=8x-3,|2x-3|=3-2x`

`pt<=>4(8x-3)+5(3-2x)=18`

`<=>32x-12+15-10x=18`

`<=>22x+3=18`

`<=>22x=15`

`<=>x=15/22(tm)`

Vậy x=15/22 hoặc x=3/14

Ta có : \(A=\sqrt{x^2-8x+20}-12=\sqrt{\left(x-4\right)^2+4}-12\)

Do \(\left(x-4\right)^2\ge0\Rightarrow\left(x+4\right)^2+4\ge4\left(\forall x\right)\)

\(\Rightarrow\sqrt{\left(x-4\right)^2+4}\ge\sqrt{4}\)

\(\Rightarrow\sqrt{\left(x-4\right)^2+4}\ge2\)

\(\Rightarrow\sqrt{\left(x-4\right)^2+4}-12\ge2-12\)

\(\Rightarrow\sqrt{\left(x-4\right)^2+4}-12\ge-10\)

\(\rightarrow A\ge-10\)

Dấu "=" xảy ra khi ( x - 4 )² =0

Suy ra x - 4 = 0 \(\rightarrow\) x = 4 .

Vậy GTNN của A là -10 khi x = 4 .