\(\left(x^2+y^2+z^2\right)\left(x+y+z\right)^2+\left(xy+yz+zx\right)^2\)
\(=\left(x^2+y^2+z^2\right)\left(x^2+y^2+z^2+2xy+2yz+2zx\right)+\left(xy+yz+zx\right)^2\)
\(=\left(x^2+y^2+z^2\right)\left[x^2+y^2+x^2+2\left(xy+yz+zx\right)\right]+\left(xy+yz+zx\right)^2\)
Gọi x2 + y2 + z2 = a, xy + yz +zx = b
Ta có:
a(a + 2b) + b2
= a2 + 2ab + b2
= (a + b)2
= (x2 + y2 + z2 + xy + yz + zx)2
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