giải pt :
\(^{^{ }6x^4}\)- \(^{35x^3}\)+ \(^{62x^2}\) - \(35x\) +6 = 0
giải các phương trình sau
b) ( x + 2)(x-3)(x + 1)(x + 6) = - 36
c) 6x4 - 35x3 + 62x2 - 35x + 6 = 0
d) x4 + x3 -4x2 + x + 1 =0
e) x4 + ( x-1)4 = 97
f) x4 -5x3 + 10x2 -10x + 4 =0
g)(x+3)4 + (x+5)4=16
b: \(\Leftrightarrow\left(x^2+3x+2\right)\left(x^2+3x-18\right)=-36\)
\(\Leftrightarrow\left(x^2+3x\right)^2-16\left(x^2+3x\right)=0\)
\(\Leftrightarrow\left(x^2+3x\right)\left(x^2+3x-16\right)=0\)
hay \(x\in\left\{0;-3;\dfrac{-3+\sqrt{73}}{2};\dfrac{-3-\sqrt{73}}{2}\right\}\)
c: \(\Leftrightarrow6x^4-18x^3-17x^3+51x^2+11x^2-33x-2x+6=0\)
\(\Rightarrow\left(x-3\right)\left(6x^3-17x^2+11x-2\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(6x^3-12x^2-5x^2+10x+x-2\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(6x^2-5x+1\right)=0\)
\(\Leftrightarrow\left(x-3\right)\left(x-2\right)\left(3x-1\right)\left(2x-1\right)=0\)
hay \(x\in\left\{3;2;\dfrac{1}{3};\dfrac{1}{2}\right\}\)
d: \(\Leftrightarrow\left(x-1\right)^2\cdot\left(x^2+3x+1\right)=0\)
hay \(x\in\left\{1;\dfrac{-3+\sqrt{5}}{2};\dfrac{-3-\sqrt{5}}{2}\right\}\)
giải các phương trình sau
b) ( x + 2)(x-3)(x + 1)(x + 6) = - 36
c) 6x4 - 35x3 + 62x2 - 35x + 6 = 0
d) x4 + x3 -4x2 + x + 1 =0
e) x4 + ( x-1)4 = 97
f) x4 -5x3 + 10x2 -10x + 4 =0
g)(x+3)4 + (x+5)4=16
giúp e với ạ >< cần gấp ạ ><
câu b nè : http://123link.pw/fGAhMX
Giải PT: X2+6X-14= \(\sqrt{98-35x+6x^2}\)
6x-1= 2x+ 3
5x(x-2)+(2x4+10x3-4x2):x2
(x + 2)2-2x-4 = 0
\(6x-1=2x+3\\ \Rightarrow4x=4\\ \Rightarrow x=1\)
\(5x\left(x-2\right)+\left(2x^4+10x^3-4x^2\right):x^2\\ =5x^2-10x+2x^2\left(2x^2+5x-4\right):x^2\\ =5x^2-10x-2\left(2x^2+5x-4\right)\\ =5x^2-10x-4x^2-10x+8\\ =x^2-20x+4\)
\(\left(x+2\right)^2-2x-4=0\\ \Rightarrow\left(x+2\right)^2-2\left(x+2\right)=0\\ \Rightarrow\left(x+2\right)\left(x+2-2\right)=0\\ \Rightarrow x\left(x+2\right)=0\\ \Rightarrow\left[{}\begin{matrix}x=0\\x=-2\end{matrix}\right.\)
Giải hệ: \(\left\{{}\begin{matrix}14x^2-21y^2-6x+45y-14=0\\35x^2+28y^241x-122y+56=0\end{matrix}\right.\)
1) Ta có: \(3x\left(2-5x\right)+35x-14=0\)
\(\Leftrightarrow3x\left(2-5x\right)+7\left(5x-2\right)=0\)
\(\Leftrightarrow-3x\left(5x-2\right)+7\left(5x-2\right)=0\)
\(\Leftrightarrow\left(5x-2\right)\left(-3x+7\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}5x-2=0\\-3x+7=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}5x=2\\-3x=-7\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{2}{5}\\x=\dfrac{7}{3}\end{matrix}\right.\)
Vậy: \(S=\left\{\dfrac{2}{5};\dfrac{7}{3}\right\}\)
2) Ta có: \(4x-6+5x\left(3-2x\right)=0\)
\(\Leftrightarrow2\left(2x-3\right)-5x\left(2x-3\right)=0\)
\(\Leftrightarrow\left(2x-3\right)\left(2-5x\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}2x-3=0\\2-5x=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}2x=3\\5x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{3}{2}\\x=\dfrac{2}{5}\end{matrix}\right.\)
Vậy: \(S=\left\{\dfrac{3}{2};\dfrac{2}{5}\right\}\)
Tìm giá trị các đa thức sau :
1. \(E=5x^7+10x^6-20x^5-35x^4+20x^3+32x+2007\) biết \(x^6+2x^5-4x^4-7x^3+4x^2-x+8=0\)
2.\(F=21x^8-24x^6+9x^5+3x^3+6x^2+2006\)biết \(7x^6-8x^4+3x^3+x+2=0\)
3.\(G=3x^4+5x^2y^2+2y^4+2x^2\)biết \(x^2+y^2=0\)
4.\(H=7x^5+8x^3y^2+35x^3y^3+40xy^5+19\)biết \(x=19\)
giải phương trình ( đoán nghiệm)
-3x4+20x3+35x2-10x+4=0
Phân tích đa thức thành nhân tử
\(e)x^3-x^2+x+3\)
\(f)2x^3-35x-75\)
\(g)3x^3-4x^2+13x-4\)
\(h)6x^3+x^2+x+1\)
\(i)4x^3+6x^2+4x+1\)