A) (X+Y+Z)3 – X3 – Y3 – Z3= (X+Y+Z-X)[(X+Y+Z)2 + X(X+Y+Z) + X2)] – (Y...
Câu 1: a) (x+y+z)
3
– x
3
– y
3
– z
3
= (x+y+z-x)[(x+y+z)
2
+ x(x+y+z) + x
2
)] – (y + z)(y
2
– yz + z
2
)
= (y + z)(3x
2
+y
2
+ z
2
+ 3xy + 2yz + 3xz – y
2
+yz –z
2
)
=3(y+z)(x
2
+xy+yz+zx) = 3(y+z)[x(x+y)+z(x+y)] = 3(x+y)(y+z)(z+x)
b) Đặt a + b – c = x, b + c – a = y, c + a – b = z => x + y + z = a + b + c.
Ta có (a+b+c)
3
– (a+b-c)
3
– (b+c-a)
3
– (c+a-b)
3
= (x + y +z)
3
– x
3
– y
3
– z
3
= 3(x+y)(y+z)(z+x) (Theo câu a))
= 3(a+b-c+b+c-a)(b+c-a+c+a-b)( c+a-b+a+b-c
=3.2b.2c.2a=24abc chia hết cho 24.
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