Toán Lớp 7: Cho a+b+c = a^2+b^2+c^2=1 và x/a= y/b= z/c (a,b,c $\ne$0)
Chứng minh rằng (x+y+z)^2= x^2+y^2+z^2
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Toán Lớp 7: Cho a+b+c = a^2+b^2+c^2=1 và x/a= y/b= z/c (a,b,c $\ne$0)
Chứng minh rằng (x+y+z)^2= x^2+y^2+z^2
Comments ( 1 )
x/a = y/b = z/c=x+y+z/a+b+c=x+y+z ( vì a+b+c=1)
=>x=a(x+y+z)=>x^2=a^2(x+y+z)^2
y=b(x+y+z)=>y^2=b^2(x+y+z)^2
z=c(x+y+z)=>z^2=c^2(x+y+z)^2
=>x^2+y^2+z^2=a^2(x+y+z)^2+b^2(x+y+z)^2+c^2(x+y+z)^2
=(x+y+z)^2(a^2+b^2+c^2)
=(x+y+z)^2 (vì a^2+b^2+c^2=1)
Vậy (x+y+z)^2= x^2+y^2+z^2