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Question

1) Rút gọn bt:(x+y+z)3+(x-y-z)3+(y-x-z)3+(z-y-x)32)Tìm x,y,z t/m: 9x2+y2+2z2-18x+4z-6y+20=0

sói nguyễn · Accepted Answer

Đặt x+y−z=a;x−y+z=b;−x+y+z=cx+y−z=a;x−y+z=b;−x+y+z=c thì a + b + c = x + y + zA=(a+b+c)3−a3−b3−c3A=(a+b+c)3−a3−b3−c3=(a+b+c−a)[(a+b+c)2+a(a+b+c)+a2]−(b3+c3)=(a+b+c−a)[(a+b+c)2+a(a+b+c)+a2]−(b3+c3)=(b+c)[a2+b2+c2+2(ab+bc+ca)+(a2+ab+ac)+a2]−(b+c)(b2−bc+c2)=(b+c)[a2+b2+c2+2(ab+bc+ca)+(a2+ab+ac)+a2]−(b+c)(b2−bc+c2)=(b+c)[3a2+b2+c2+3ab+2bc+3ac−b2+bc−c2]=(b+c)[3a2+b2+c2+3ab+2bc+3ac−b2+bc−c2]=(b+c)(3a2+3ab+3bc+3ca)=(b+c)(3a2+3ab+3bc+3ca)=(b+c)(3a(a+b)+3c(a+b))=3(a+b)(b+c)(c+a)Câu trả lời: Đặt x+y−z=a;x−y+z=b;−x+y+z=cx+y−z=a;x−y+z=b;−x+y+z=c thì a + b + c = x + y + zA=(a+b+c)3−a3−b3−c3A=(a+b+c)3−a3−b3−c3=(a+b+c−a)[(a+b+c)2+a(a+b+c)+a2]−(b3+c3)=(a+b+c−a)[(a+b+c)2+a(a+b+c)+a2]−(b3+c3)=(b+c)[a2+b2+c2+2(ab+bc+ca)+(a2+ab+ac)+a2]−(b+c)(b2−bc+c2)=(b+c)[a2+b2+c2+2(ab+bc+ca)+(a2+ab+ac)+a2]−(b+c)(b2−bc+c2)=(b+c)[3a2+b2+c2+3ab+2bc+3ac−b2+bc−c2]=(b+c)[3a2+b2+c2+3ab+2bc+3ac−b2+bc−c2]=(b+c)(3a2+3ab+3bc+3ca)=(b+c)(3a2+3ab+3bc+3ca)=(b+c)(3a(a+b)+3c(a+b))=3(a+b)(b+c)(c+a)

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