来自沈兆勇的问题
【1.已知a*x^3=b*y^3=c*z^3且1/x+1/y+1/z=1求证(a*x^2+b*y^2+c*z^2)^(1/3)=a^(1/3)+b^(1/3)+c^(1/3){提示令a*x^3=b*y^3=c*z^3=T则a*x^2=T/Xb*y^2=T/Yc*z^2=T/Z}2.已知实数a,b满足a-3*a^(2/3)+5*a^(1/3)=5b-3*b^(2/3)+5*b^(1/3)=5求证a^(1/3)+b^】
1.已知a*x^3=b*y^3=c*z^3且1/x+1/y+1/z=1求证(a*x^2+b*y^2+c*z^2)^(1/3)=a^(1/3)+b^(1/3)+c^(1/3){提示令a*x^3=b*y^3=c*z^3=T则a*x^2=T/Xb*y^2=T/Yc*z^2=T/Z}
2.已知实数a,b满足a-3*a^(2/3)+5*a^(1/3)=5b-3*b^(2/3)+5*b^(1/3)=5求证a^(1/3)+b^(1/3)=2
