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)
cho x+y+z=0. CMR:
\(2.\left(x^5+y^5+z^5\right)=5xyz.\left(x^2+y^2+z^2\right)\)
cho x + y+z=0. cmr 2(x^5+y^5+z^5)=5xyz(x^2+y^2+z^2)
cho a+b+c=0;a^2+b^2+c^2=0;a^3+b^3+c^3=0. tính a+b^2+c^3
Cho :\(x+y+z=0\) . CMR: \(2\left(x^5+y^5+z^5\right)=5xyz\left(x^2+y^2+z^2\right)\)
cho x+y+z=0. cm \(2\left(x^5+y^5+z^5\right)=5xyz\left(x^2+y^2+z^2\right)\)
Câu 5 cho x+y+z = 0 chứng minh
2(x^5+y^5+z^5) = 5xyz(x^2+y^2+z^2)
Cho x+y+z=0
Chứng minh 2(x^5+y^5+z^5) = 5xyz(x^2+y^2+z^2)
Cho a+b+c=0
CMR:2(x5+y5+z5)=5xyz(x2+y2+z2)
Cho x+y+z = 0. CMR :
a) 5( x3 + y3 + z3 ) (x2 + y2 + z2) = 6(x5 + y5 + z5 )
b) 2( x5 + y5 + z5 ) = 5xyz( x2 + y2 + z2 )
Cho x+y+z=0. CM:
\(2\left(x^5+y^5+z^5\right)=5xyz\left(x^2+y^2+z^2\right)\)