a: =>x^3-3x^2+3x^2-9x+4x-12+a+12 chia hết cho x-3

=>a+12=0

=>a=-12

b: =>2x^2-6x+5x-15+a+15 chia hết cho x-3

=>a+15=0

=>a=-15

c: =>x^3-2x^2-5x^2+20+a-20 chia hết cho x-2

=>a-20=0

=>a=20

e: =>10x^2-15x+8x-12+a+12 chia hết cho 2x-3

=>a+12=0

=>a=-12

f: =>5x^3-x^2+5x^2-x-5x+1-a-1 chia hết cho 5x-1

=>-a-1=0

=>a=-1

\(A\left(x\right)=5x^3+3x^2-x-7\)

\(B\left(x\right)=7x^3-3x+4\)

=>\(5x^3+3x^2-x-7=7x^3-3x+4\)

\(\Leftrightarrow-2x^3+3x^2+2x-11=0\)

hay \(x\in\left\{-1.52\right\}\)

\(E=5x^7+10x^6-20x^5-35x^4+20x^3-5x^2+40x+105\)

\(=\left(5x^7+10x^6-20x^5-35x^4+20x^3-5x^2+40x\right)+105\)

\(=5x\left(x^6+2x^5-4x^4-7x^3+4x^2-x+8\right)+105\)

Thay \(x^6+2x^5-4x^4-7x^3+4x^2-x+8=0\)vào đa thức ta được:

\(E=5x.0+105=105\)

a.\(2x^2+5x+8+\sqrt{x}=x^2+3x+35+x^2+2x-7\)

\(=2x^2+5x+8+\sqrt{x}=2x^2+5x+28\Leftrightarrow\sqrt{x}=20\Leftrightarrow x=400.\)

b.\(3\sqrt{x}+7x+5=\sqrt{x}+4x-6+3x+18\)

\(=3\sqrt{x}+7x+5=\sqrt{x}+7x+12\Leftrightarrow2\sqrt{x}=7\Leftrightarrow x=\frac{49}{4}.\)

c.\(8\sqrt{x}+2x-9=5x+7+6\sqrt{x}-3x-12.\)

\(=8\sqrt{x}+2x-9=2x+6\sqrt{x}-5\Leftrightarrow2\sqrt{x}=4\Leftrightarrow x=4.\)

d.\(2\sqrt{3x}+11x-18=5x+3+6\sqrt{3x}+6x-21\)

\(=2\sqrt{3x}+11x-18=11x+6\sqrt{3x}-19\Leftrightarrow4\sqrt{3x}=1\)

\(\Leftrightarrow\sqrt{3x}=\frac{1}{4}\Leftrightarrow3x=\frac{1}{16}\Leftrightarrow x=\frac{1}{48}.\)

a) \(2x^2+5x+8+\sqrt{x}=x^2+3x+35+x^2+2x-7\)

<=> \(2x^2+5x+8+\sqrt{x}=2x^2+5x+28\)

<=> \(2x^2+5x+8+\sqrt{x}-\left(2x^2+5\right)=28\)

<=> \(\sqrt{x}+8=28\)

<=> \(\sqrt{x}=28-8\)

<=> \(\sqrt{x}=20\)

<=> \(\left(\sqrt{x}\right)^2=20^2\)

<=> x = 400

=> x = 400

b) \(3\sqrt{x}+7x+5=\sqrt{x}+4x-6+3x+18\)

<=> \(3\sqrt{x}+7x+5=7x+\sqrt{x}+12\)

<=> \(3\sqrt{x}+5=7x+\sqrt{x}+12-7x\)

<=> \(3\sqrt{x}+5=\sqrt{x}+12\)

<=> \(3\sqrt{x}=\sqrt{x}+12-5\)

<=> \(3\sqrt{x}=\sqrt{x}+7\)

<=> \(3\sqrt{x}-\sqrt{x}=7\)

<=> \(2\sqrt{x}=7\)

<=> \(\sqrt{x}=\frac{7}{2}\)

<=> \(\left(\sqrt{x}\right)^2=\left(\frac{7}{2}\right)^2\)

<=> \(x=\frac{49}{4}\)

=> \(x=\frac{49}{4}\)

c) \(8\sqrt{x}+2x-9=5x+7+6\sqrt{x}-3x-12\)

<=> \(8\sqrt{x}+2x-9=2x+6\sqrt{x}-5\)

<=> \(8\sqrt{x}-9=2x+6\sqrt{x}-5-2x\)

<=> \(8\sqrt{x}-9=6\sqrt{x}-5\)

<=> \(8\sqrt{x}=6\sqrt{x}-5+9\)

<=> \(8\sqrt{x}=6\sqrt{x}+4\)

<=> \(8\sqrt{x}-6\sqrt{x}=4\)

<=> \(2\sqrt{x}=4\)

<=> \(\sqrt{x}=2\)

<=> \(\left(\sqrt{x}\right)^2=2^2\)

<=> x = 4

=> x = 4

d) \(2\sqrt{3x}+11x-18=5x+3+6\sqrt{3x}+6x-21\)

<=> \(2\sqrt{3x}+11x-18=11x+6\sqrt{3x}-18\)

<=> \(2\sqrt{3x}+11x-18-\left(11x-18\right)=6\sqrt{3x}\)

<=>\(2\sqrt{3x}=6\sqrt{3x}\)

<=> \(2\sqrt{3x}-6\sqrt{3x}=0\)

<=>\(-4\sqrt{3x}=0\)

<=> \(\sqrt{3x}=0\)

<=> \(\left(\sqrt{3x}\right)^2=0^2\)

<=> 3x = 0

<=> x = 0

=> x = 0

a: 4x+9=0

=>4x=-9

=>x=-9/4

b: -5x+6=0

=>-5x=-6

=>x=6/5

c: 7-2x=0

=>2x=7

=>x=7/2

d: 2x+5=0

=>2x=-5

=>x=-5/2

e: 2x+6=0

=>2x=-6

=>x=-3

g: 3x-1/4=0

=>3x=1/4

hay x=1/12

à, phần a ra x = 400. Nhầm

Dạng 1:

a) $4x+9=4x+\frac{9}{4}.4=4(x+\frac{9}{4}\Rightarrow$ Nghiệm là $-\frac{9}{4}$

b) $-5x+6=-5x+(-5).(-\frac{6}{5})=-5(x-\frac{6}{5})\Rightarrow$ Nghiệm là $\frac{6}{5}$

c) $7-2x=-2x+7=-2x+(-2).(-\frac{7}{2})=-2(x-\frac{7}{2})\Rightarrow$ Nghiệm là $\frac{7}{2}$

d) $2x+5=2x+2.\frac{5}{2}=2.(x+\frac{5}{2})\Rightarrow$ Nghiệm là $-\frac{5}{2}$

e) $2x+6=2x+2.3=2(x+3)\Rightarrow$ Nghiệm là -3

g) $3x-\frac{1}{4}=3x-3.(\frac{1}{12})=3(x-\frac{1}{12})\Rightarrow$ Nghiệm là $\frac{1}{12}$

h) $3x-9=3x-3.3=3(x-3)\Rightarrow$ Nghiệm là 3

k) $-3x-\frac{1}{2}=-3x-3.(\frac{1}{6})=-3(x+\frac{1}{6})\Rightarrow$ Nghiệm là $-\frac{1}{6}$

m) $-17x-34=-17x-17.2=-17(x+2)\Rightarrow$ Nghiệm là -2

n) $2x-1=2x+2.(-\frac{1}{2})=3(x-\frac{1}{2})\Rightarrow$ Nghiệm là $\frac{1}{2}$

q) $5-3x=-3x+5=-3x+(-3).(-\frac{5}{3})=-3(x-\frac{5}{3})\Rightarrow$ Nghiệm là $\frac{5}{3}$

p) $3x-6=3x+3.(-2)=3(x-2)\Rightarrow$ Nghiệm là 2

Cảm ơn nhiều nhiều nhiều :3