Câu 5 cho x+y+z = 0 chứng minh
2(x^5+y^5+z^5) = 5xyz(x^2+y^2+z^2)
Những câu hỏi liên quan
Cho x+y+z=0
Chứng minh 2(x^5+y^5+z^5) = 5xyz(x^2+y^2+z^2)
Chứng minh rằng nếu x+y+z=0 thì:2 (x^5+y^5+z^5)=5xyz(x^2+y^2+z^2)
Vì x+y+z=0
=>x+y=-z =>(x+y)^5=-z^5
hay x^5+y^5+5(x^4y+xy^4+2x³y²+2x²y³+)=-z^5
<=>x^5+y^5+z^5+5xy(x³+y³+2x²y+2x²y)=0
<=>x5+y^5+z^5+5xy(x+y)(x²-xy+y²+2xy)=0
<=>x^5+y^5+z^5-5xyz(x²+xy+y²)=0
<=>x^5+y^5+z^5=5xyz(x²+xy+y²)
<=>2(x^5+y^5+z^5)=5xyz(2x²+2xy+2y²)
<=>2(x^5+y^5+z^5)=5xyz[x²+y²+(x+y)²]
<=>2(x^5+y^5+z^5)=5xyz(x³+y²+z²)
Đúng 0
Bình luận (0)
Chứng minh rằng nếu x+y+z =0
Thì x^5+y^5+z^5=5xyz(x^2+y^2+z^2)
Cho\(x+y+z=0.\) Chứng minh rằng: \(2\left(x^5+y^5+z^5\right)=5xyz\left(x^2+y^2+z^2\right).\)
Cho x+y+z=0.
Chứng minh rằng : 2(x5 + y5 +z5)=5xyz(x2 + y2 + z2)
\(y+z=-x\)
\(\Leftrightarrow\left(y+z\right)^5=-x^5\)
\(\Leftrightarrow y^5+5y^4z+10y^3z^2+10y^2z^3+5yz^4+z^5+x^5=0\)
\(\Leftrightarrow x^5+y^5+z^5+5yz\left(y^3+2y^2z+2yz^2+z^3\right)=0\)
\(\Leftrightarrow x^5+y^5+z^5+5yz\left[\left(y+z\right)\left(y^2-yz-z^2\right)+2yz\left(y+z\right)\right]=0\)
\(\Leftrightarrow x^5+y^5+z^5+5yz\left(y+z\right)\left(y^2+yz+z^2\right)=0\)
\(\Leftrightarrow2\left(x^5+y^5+z^5\right)-5xyz\left[\left(y^2+2yz+z^2\right)+y^2+z^2\right]=0\)
\(\Leftrightarrow2\left(x^5+y^5+z^5\right)=5xyz\left(x^2+y^2+z^2\right)\)(đpcm)
Đúng 0
Bình luận (0)
Chứng minh rằng nếu x + y + z =0 thì 2(x5 + y5 + z5) = 5xyz(x2 + y2 + z2).
Chứng minh rằng nếu x+y+z =0 thì
\(2\left(x^5+y^5+z^5\right)=5xyz\left(x^2+y^2+z^2\right)\)
Ta có: x+y+z=0
=>x+y=-z =>(x+y)^5=-z^5
hay x^5+y^5+5(x^4y+xy^4+2x³y²+2x²y³+)=-z^5
<=>x^5+y^5+z^5+5xy(x³+y³+2x²y+2x²y)=0
<=>x5+y^5+z^5+5xy(x+y)(x²-xy+y²+2xy)=0
<=>x^5+y^5+z^5-5xyz(x²+xy+y²)=0
<=>x^5+y^5+z^5=5xyz(x²+xy+y²)
<=>2(x^5+y^5+z^5)=5xyz(2x²+2xy+2y²)
<=>2(x^5+y^5+z^5)=5xyz[x²+y²+(x+y)²]
<=>2(x^5+y^5+z^5)=5xyz(x³+y²+z²)
Từ x+y+z=0 => y+z=-x => (y+z)5=-x5
=> \(y^5+5y^4z+10y^2z^2+10y^2z^3+5yz^4+z^5=-x^5\)
\(\Rightarrow\left(x^5+y^5+z^5\right)+5yz\left(y^3+2y^2z+2yz^2+z^3\right)=0\)
\(\Rightarrow\left(x^5+y^5+z^5\right)+5yz\left[\left(y+z\right)\left(y^2-yz+x^2\right)\right]=0\)
\(\Rightarrow\left(x^5+y^5+z^5\right)+5yz\left(y+z\right)\left(y^2+yz+z^2\right)=0\)
\(\Rightarrow2\left(x^5+y^5+z^5\right)-5xyz\left[\left(y^2+2yz+z^2\right)+y^2+z^2\right]=0\)
\(\Rightarrow2\left(x^5+y^5+z^5\right)=5xyz\left[\left(y+z\right)^2+y^2+z^2\right]\) (đpcm)
Chứng minh rằng nếu x+y+z=0 thì
\(2\left(x^5+y^5+z^5\right)=5xyz\left(x^2+y^2+z^2\right)\)
https://hoc24.vn/hoi-dap/question/175259.html
Vào link coi, t làm mất công ngta kêu chép nx..Mệt lắm !
Cho x+y+z=0. CMR 2(x^5+y^5+z^5)=5xyz(x^2+y^2+z^2)
x + y + z = 0
⇒x3+y3+z3=3xyz⇒x3+y3+z3=3xyz
⇒(x3+y3+z3)(x2+y2+z2)=3xyz(x2+y2+z2)⇒(x3+y3+z3)(x2+y2+z2)=3xyz(x2+y2+z2)
⇒x5+y5+z5+x2y2(x+y)+y2z2(y+z)+z2x2(z+x)=3xyz(x2+y2+z2)⇒x5+y5+z5+x2y2(x+y)+y2z2(y+z)+z2x2(z+x)=3xyz(x2+y2+z2)
⇒x5+y5+z5−xyz(xy+yx+zx)=3xyz(x2+y2+z2)⇒x5+y5+z5−xyz(xy+yx+zx)=3xyz(x2+y2+z2)
⇒2(x5+y5+z5)=5xyz(x2+y2+z2)
Đúng 1
Bình luận (0)