P(x)=3x^4 + x^2 - 3x^4 + 5
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b, \(\left(x-5\right)\left(x-4\right)-\left(x+1\right)\left(x-2\right)=7\)
\(\Rightarrow x^2-9x+20-x^2+x+2=7\)
\(\Rightarrow-8x+22=7\)
\(\Rightarrow-8x=-15\)
\(\Rightarrow x=\frac{15}{8}\)
c, \(\left(3x-4\right)\left(x-2\right)=3x\left(x-9\right)-3\)
\(\Rightarrow3x^2-10x+8=3x^2-27x-3\)
\(\Rightarrow3x^2-10x-3x^2+27x=\left(-3\right)+\left(-8\right)\)
\(\Rightarrow17x=-11\)
\(\Rightarrow x=-\frac{11}{17}\)
d, \(\left(x-3\right)\left(x^2+3x+9\right)+x\left(5-x^2\right)=6x\)
\(\Rightarrow x^3+3x^2+9x-3x^2-9x-27+5x-x^3=6x\)
\(\Rightarrow6x=-27\)
\(\Rightarrow x=-\frac{27}{6}\)
\(\Rightarrow x=-\frac{9}{2}\)
e, \(\left(3x-5\right)\left(x+1\right)-\left(3x-1\right)\left(x+1\right)=x-4\)
\(\Rightarrow3x^2-2x-5-3x^2-2x+1=x-4\)
\(\Rightarrow-4=x-4\)
\(\Rightarrow x=0\)
b) (x - 5)(x - 4) - (x + 1)(x - 2) = 7
<=> x2 - 9x + 20 - x2 + x + 2 - 7 = 0
<=> 8x - 15 = 0 <=> x = 15/8
c) (3x - 4)(x - 2) = 3x(x - 9) - 3
<=> 3x2 - 10x + 8 = 3x2 - 27x - 3
<=> 17x = -11 <=> x = -11/17
d) (x - 3)(x2 + 3x + 9) + x(5 - x2) = 6x
<=> x3 - 27 - x3 + 5x - 6x = 0
<=> x = -27
e) (3x - 5)(x + 1) - (3x - 1)(x + 1) = x - 4
<=> (x + 1)(3x - 5 - 3x + 1) - x + 4 = 0
<=> -4x - 4 - x + 4 = 0 <=> x = 0
b) \(\left(x-5\right)\left(x-4\right)-\left(x+1\right)\left(x-2\right)=7\)
\(\Leftrightarrow\) \(x^2-4x-5x+20-x^2+2x-x+2\)\(=7\)
\(\Leftrightarrow\) \(-8x+22=7\)
\(\Leftrightarrow\) x= \(\frac{-15}{8}\)
1: \(=6x^2+2x-15x-5-x^2+6x-9+4x^2+20x+25-27x^3-27x^2-9x-1\)
=-27x^3-18x^2+4x+10
2: =4x^2-1-6x^2-9x+4x+6-x^3+3x^2-3x+1+8x^3+36x^2+54x+27
=7x^3+37x^2+46x+33
5:
\(=25x^2-1-x^3-27-4x^2-16x-16-9x^2+24x-16+\left(2x-5\right)^3\)
\(=8x^3-60x^2+150-125+12x^2-x^3+8x-60\)
=7x^3-48x^2+8x-35
a, \(4x\left(x-5\right)-7x\left(x-4\right)+3x^2=12\)
\(\Leftrightarrow4x^2-20x-7x^2+28x+3x^2=12\)
\(\Leftrightarrow8x=12\)
\(\Leftrightarrow x=\dfrac{3}{2}\)
Vậy...
b, \(-3x\left(x-5\right)+5\left(x-1\right)+3x^2=4-x\)
\(\Leftrightarrow-3x^2+15x+5x-5+3x^2=4-x\)
\(\Leftrightarrow21x=9\)
\(\Leftrightarrow x=\dfrac{3}{7}\)
Vậy...
c, \(\left(x-5\right)\left(x-4\right)-\left(x+1\right)\left(x-2\right)=7\)
\(\Leftrightarrow x^2-9x+20-x^2+x+2=7\)
\(\Leftrightarrow-8x=-15\Leftrightarrow x=\dfrac{15}{8}\)
Vậy...
d, \(-\left(x+3\right)\left(x-4\right)+\left(x-1\right)\left(x+1\right)=10\)
\(\Leftrightarrow-x^2+x+12+x^2-1=10\)
\(\Leftrightarrow x=-1\)
Vậy...
e, \(\left(x-3\right)\left(x^2+3x+9\right)+x\left(5-x^2\right)=6x\)
\(\Leftrightarrow x^3-27+5x-x^3=6x\)
\(\Leftrightarrow x=-27\)
Vậy...
a) \(4x\left(x-5\right)-7x\left(x-4\right)+3x^2=12\)
\(4x^2-20x-7x^2+28x+3x^2-12=0\)
\(8x-12=0\)
\(4\left(2x-3\right)=0\)
\(2x-3=0\Rightarrow x=\dfrac{3}{2}\)
b) \(-3x\left(x-5\right)+5\left(x-1\right)+3x^2=4-x\)
\(-3x^2+15x+5x-5+3x^2-4+x=0\)
\(21x-9=0\)
\(3\left(7x-3\right)=0\)
\(\Rightarrow7x-3=0\Rightarrow x=\dfrac{3}{7}\)
c) \(\left(x-5\right)\left(x-4\right)-\left(x-1\right)\left(x-2\right)=7\)
\(x^2-4x-5x+20-x^2+2x+x-2-7=0\)
\(-6x+11=0\Rightarrow x=\dfrac{11}{6}\)
d) \(-\left(x-3\right)\left(x-4\right)+\left(x-1\right)\left(x+1\right)=10\)
\(-x^2+4x+3x-12+x^2-1-10=0\)
\(7x-23=0\)
\(x=\dfrac{23}{7}\)
e) \(\left(x-3\right)\left(x^2+3x+9\right)+x\left(5-x^2\right)=6x\)
\(x^3-27+5x-x^3-6x=0\)
\(-x-27=0\Rightarrow x=-27\)
a) (3x + 1)^2 - 2(3x + 1)(3x - 5) + (3x - 5)^2
= 9x^2 + 6x + 1 - 18x^2 + 24x + 10 + 9x^2 - 30x + 25
= 36
b) (3x^2 - y)^2
= 9x^4 - 6x^2y + y^2
c) (3x + 5)^2 + (3x - 5)^2 - (3x + 2)(3x - 2)
= 9x^2 + 30x + 25 + 9x^2 - 30x + 25 - 9x^2 + 4
= 9x^2 + 54
d) 2x(2x - 1)^2 - 3x(x + 3)(x - 3) - 4x(x + 1)^2
= 8x^3 - 8x^2 + 2x - 3x^2 + 27x - 4x^3 - 8x^2 - 4x
= x^3 - 16x^2 + 25x
e) (x - 2)(x^2 + 2x + 4) - (x + 1)^2 + 3(x - 1)(x + 1)
= x^3 - 8 - x^2 - 2x - 1 + 3x^2 - 2
= x^3 + 2x^2 - 2x - 12
f) (x^4 - 5x^2 + 25)(x^2 + 5) - (2 + x^2)^2 + 3(1 + x^2)^2
= x^6 + 125 - 4 - 4x^2 - x^2 + 3 + 6x^2 + 3x^4
= x^6 + 2x^4 + 2x^2 + 124
Tìm x biết:
b/\(\left(2x+3\right)^2-\left(5x-4\right)\left(5x+4\right)=\left(x+5\right)^2-\left(3x-1\right)\left(7x+2\right)-\left(x^2-x+1\right)\)
<=> \(4x^2 +12x+9-25x^2+16-x^2-10x-25+21x^2+6x-7x-2+x^2-x+1=0\)
<=>0x-1=0
<=>0x=1 (vô lí) (dòng này không cần ghi thêm cũng được)
=> Không có giá trị x nào thỏa mãn
c/ \((1-3x)^2-(x-2)(9x+1)=(3x-4)(3x+4)-9(x+3)^2\)
<=>\(1-6x+9x^2-9x^2-x+18x+2-9x^2+16+9x^2+54x+81=0\)
<=> 65x+100=0
<=> x=\(\dfrac{-20}{13}\)
d/\((3x+4)(3x-4)-(2x+5)^2=(x-5)^2+(2x+1)^2-(x^2-2x)+(x-1)^2\)
<=> \(9x^2-16-4x^2-20x-25-x^2+10x-25-4x^2-4x-1+x^2+2x-x^2+2x-1=0\)
<=> -10x-68=0
<=> x=\(\dfrac{-34}{5}\)
\(\frac{3}{x+1}+\frac{2}{x+2}=\frac{5x+4}{x^2+3x+2}.\)ĐKXĐ: \(x\ne-1;-2\)
\(\Leftrightarrow\frac{3\left(x+2\right)}{\left(x+1\right)\left(x+2\right)}+\frac{2\left(x+1\right)}{\left(x+1\right)\left(x+2\right)}=\frac{5x+4}{\left(x+1\right)\left(x+2\right)}\)
\(\Leftrightarrow3x+6+2x+2=5x+4\)
\(\Leftrightarrow3x+2x-5x=-6-2+4\)
\(\Leftrightarrow0x=-4\)
=> PT vô nghiệm
\(2;\frac{2}{3x-1}-\frac{15}{6x^2-x-1}=\frac{3}{2x-1}\)
\(\Leftrightarrow\frac{2\left(2x-1\right)}{\left(2x-1\right)\left(3x-1\right)}-\frac{15}{6x^2+3x-2x-1}=\frac{3\left(3x-1\right)}{\left(2x-1\right)\left(3x-1\right)}\)
\(\Leftrightarrow\frac{4x-2-15}{\left(2x-1\right)\left(3x-1\right)}=\frac{9x-3}{\left(2x-1\right)\left(3x-1\right)}\)
\(\Leftrightarrow4x-2-15=9x-3\)
\(\Leftrightarrow4x-9x=2+15-3\)
\(\Leftrightarrow-5x=14\)
.....
P(x) = 3x4 + x2 - 3x4 + 5
P(x) = (3x4 - 3x4) + x2 + 5
P(x) = x2 + 5
p(x) =3x^4 + x^2 - 3x^4 + 5
p(x) = (3^4 - 3x^4) + x2 +5
p(x) = x^2 + 5
=> p(x) = x^2 + 5