两道高二关于基本不等式的题(1)已知x、y属于正实数求证:(x+y)(x²+y²)(x³+y³)≥8x³y³(2)当a>0 b>0时求证:(b/a)+(2/b)≥2第二题打错了(2)当a>0 b>0时 求证:(b/a)+
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![两道高二关于基本不等式的题(1)已知x、y属于正实数求证:(x+y)(x²+y²)(x³+y³)≥8x³y³(2)当a>0 b>0时求证:(b/a)+(2/b)≥2第二题打错了(2)当a>0 b>0时 求证:(b/a)+](/uploads/image/z/14527557-45-7.jpg?t=%E4%B8%A4%E9%81%93%E9%AB%98%E4%BA%8C%E5%85%B3%E4%BA%8E%E5%9F%BA%E6%9C%AC%E4%B8%8D%E7%AD%89%E5%BC%8F%E7%9A%84%E9%A2%98%EF%BC%881%EF%BC%89%E5%B7%B2%E7%9F%A5x%E3%80%81y%E5%B1%9E%E4%BA%8E%E6%AD%A3%E5%AE%9E%E6%95%B0%E6%B1%82%E8%AF%81%EF%BC%9A%EF%BC%88x%2By%29%28x%26sup2%3B%2By%26sup2%3B%29%28x%26sup3%3B%2By%26sup3%3B%29%E2%89%A58x%26sup3%3By%26sup3%3B%EF%BC%882%EF%BC%89%E5%BD%93a%EF%BC%9E0+b%EF%BC%9E0%E6%97%B6%E6%B1%82%E8%AF%81%EF%BC%9A%EF%BC%88b%2Fa%29%2B%282%2Fb%29%E2%89%A52%E7%AC%AC%E4%BA%8C%E9%A2%98%E6%89%93%E9%94%99%E4%BA%86%EF%BC%882%EF%BC%89%E5%BD%93a%EF%BC%9E0+b%EF%BC%9E0%E6%97%B6+%E6%B1%82%E8%AF%81%EF%BC%9A%EF%BC%88b%2Fa%29%2B)
两道高二关于基本不等式的题(1)已知x、y属于正实数求证:(x+y)(x²+y²)(x³+y³)≥8x³y³(2)当a>0 b>0时求证:(b/a)+(2/b)≥2第二题打错了(2)当a>0 b>0时 求证:(b/a)+
两道高二关于基本不等式的题
(1)已知x、y属于正实数
求证:(x+y)(x²+y²)(x³+y³)≥8x³y³
(2)当a>0 b>0时
求证:(b/a)+(2/b)≥2
第二题打错了
(2)当a>0 b>0时
求证:(b/a)+(a/b)≥2
两道高二关于基本不等式的题(1)已知x、y属于正实数求证:(x+y)(x²+y²)(x³+y³)≥8x³y³(2)当a>0 b>0时求证:(b/a)+(2/b)≥2第二题打错了(2)当a>0 b>0时 求证:(b/a)+
(1)求证:(x+y)(x²+y²)(x³+y³)≥8x³y³
证明:①(x+y)≥2√xy
②(x^2+y^2)≥2xy
③(x^3+y^3)≥2xy√xy
①②③相乘
(x+y)(x^2+y^2)(x^3+y^3)≥2√xy*2xy*2xy√xy
(x+y)(x^2+y^2)(x^3+y^3)≥8x^3y^3
(2)当a>0 b>0时
求证:(b/a)+(a/b)≥2
证明:a>0 b>0可用均值不等式
(b/a)+(a/b)≥2√(b/a)*(a/b)=2√1=2
即:(b/a)+(a/b)≥2
1. 我们知道:a2+b2≥2ab
X+Y=(X1/2)2+(Y1/2)2≥2X1/2Y1/2
X3+Y3=(X3/2)2+(Y3/2)2≥2X3/2Y3/2
因此,可得::(x+y)(x²+y²)(x³+y³)≥8x³y³
2.命题错误,如a=b=4,则等式显然不成立。
(1)已知x、y属于正实数
求证:(x+y)(x²+y²)(x³+y³)≥8x³y³
由a+b≥2(ab)^1/2
左边≥2(xy)^1/2*[(xy)^2]^1/2*[(xy)^3]^1/2
=8x³y³
(2)当a>0 b>0时
求证:(b/a)+(2/...
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(1)已知x、y属于正实数
求证:(x+y)(x²+y²)(x³+y³)≥8x³y³
由a+b≥2(ab)^1/2
左边≥2(xy)^1/2*[(xy)^2]^1/2*[(xy)^3]^1/2
=8x³y³
(2)当a>0 b>0时
求证:(b/a)+(2/b)≥2
是不是:(b/a)+(a/b)≥2
如果是的话左边≥2[(b/a)*(a/b)]^1/2=2
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