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\(1,4x\left(x-5\right)-\left(x-1\right)\left(4x-3\right)=5\)
\(4x^2-20x-4x^2+3x-4x+3=5\)
\(-21x+3=5\)
\(21x=-8\)
\(x=-\frac{8}{21}\)
\(2,8x^3-50x=0\)
\(x\left(8x^2-50\right)=0\)
\(\Rightarrow\hept{\begin{cases}x=0\\8x^2-50=0\Rightarrow x=\pm2\end{cases}}\)
Vậy ....
\(3,\left(2x-1\right)^2-25=0\)
\(\left(2x-1\right)^2=\pm5^2\)
\(\Rightarrow\hept{\begin{cases}2x-1=5\\2x-1=\left(-5\right)\end{cases}}\Rightarrow\hept{\begin{cases}x=3\\x=\left(-2\right)\end{cases}}\)
Vậy ...
a) Theo định lí Bezout ta có:
\(f\left(-5\right)=3.\left(-5\right)^2-5a+27=2\)
\(\Leftrightarrow75-5a+27=2\)
\(\Leftrightarrow102-5a=2\)
\(\Rightarrow a=20\)
b) \(x^3+ax^2+x+b=\left(x^2-x+2\right).\left(x+m\right)\)(Trong đó m là số nguyên)
\(\Leftrightarrow x^3+ax^2+x+b=x^3+x^2.\left(m-1\right)-mx+2m\)
Sử dụng phương pháp đồng nhất hệ số ta có:
\(\hept{\begin{cases}ax^2=m-1\\x=-mx\\2m=b\end{cases}}\Leftrightarrow\hept{\begin{cases}a=m-1\\m=-1\\2m=b\end{cases}}\Leftrightarrow\hept{\begin{cases}a=-2\\b=-2\end{cases}}\Leftrightarrow a=b=-2\)
Trả lời:
a, \(-xy.\left(x^2+2xy-3\right)=-x^3y-2x^2y^2+3xy\)
b, \(\left(12x^6y^5-3x^3y^4+4x^2y\right):6x^2y\)
\(=12x^6y^5:6x^2y^2-3x^3y^4:6x^2y+4x^2y+6x^2y\)
\(=2x^4y^3-\frac{1}{2}xy^3+\frac{2}{3}\)
a.\(\left(-xy\right)\left(x^2+2xy-3\right)=-x^3y-2x^2y^2+6xy\)
b.\(\left(12x^6y^5-3x^3y^4+4x^2y\right):6x^2y=2x^4y^4-\frac{1}{2}xy^3+\frac{2}{3}\)
- a, [x^2.(x-3)-(x-3)] :( x-3) = (x-3 ).(x^2-1) : (x-3) =X^2-1
2 b, (x-y-z)^5-3 = (x-y-z)^2
3 c, x^2-1
4 d, 2x^4 + x^2 - 6x^2 + x^3 - 3 - 3x / x^2 - 3
= x^2(2x^2 + x + 1) - 3(2x^2 + x + 1) / x^2 - 3
= (2x^2 + x + 1)(x^2 - 3) / x^2 - 3
= 2x^2 + x + 1
5 e, 2.(x-1)
6 f, (2x3 – 5x2 + 6x – 15) : (2x – 5)
=(2x3−5x2)+(6x−15)=(2x3−5x2)+(6x−15)
=x2(2x−5)+3(2x−5)=x2(2x−5)+3(2x−5)
=(x2+3)(2x−5)=(x2+3)(2x−5)
=(2x3−5x2+6x−15):(2x−5)=x2+3
Bài 1:a. (x+3)2−(x−4)(x+8)=1⇔x2+6x+9−x2−4x+32=1⇔2x=−40⇔x=20Vậy S={20}b. 4x−20+3x−15=0⇔7x=35⇔x=5Vậy S={5}c. x3−5x2+25x+5x2−25x+125−x3=5x⇔5x=125⇔x=25Vậy S={25}d. 4x2+4x+1−4x2+9=22⇔4x=12⇔x=3Vậy S={3}e. 3x−3−1+x=0⇔4x=4⇔x=1Vậy S={1}f. x2(x+3)−5(x+3)=0⇔(x+3)(x2−5)=0⇔x=−3; x=±√5Vậy S={−3; ±√5}Bài 2:a. x2−6x+9=0⇔(x−3)2=0⇔x=3Vậy S={3}b. 8x3−12x2+6x−1=0⇔(2x−1)3=0⇔x=12Vậy S={12}c. x3+4x2+4x=0⇔x(x2+4x+4)=0⇔x(x+2)2=0⇔x=0; x=−2Vậy S={−2;0}d. 4x3−36x=0⇔4x(x2−9)=0⇔x=0; x=±3Vậy S={0;±3}e. x3+5x2−4x−20=0⇔(x−2)(x+2)(x+5)=0⇔x=±2; x=−5Vậy S={±2;−5}f. 2x2+16x+32−x2+4=0⇔x2+16x+36=0⇔(x+8)2=28⇔x=−8±2√7Vậy S={−8±2√7}g.x3−27+4x−x3=0⇔4x=27⇔x=274Vậy S={274}h. x2+5x−14=0⇔(x−2)(x+7)=0⇔x=2; x=−7Vậy S={2;−7}