较难不等式证明已知 :a > 0,b > 0,a + b = 1 .求证 :(a + 1/a )^2 *( b + 1/b )^2≥ 25/2 .抱歉 :求证 :(a + 1/a )^2 + ( b + 1/b )^2≥ 25/2 .
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![较难不等式证明已知 :a > 0,b > 0,a + b = 1 .求证 :(a + 1/a )^2 *( b + 1/b )^2≥ 25/2 .抱歉 :求证 :(a + 1/a )^2 + ( b + 1/b )^2≥ 25/2 .](/uploads/image/z/13327200-0-0.jpg?t=%E8%BE%83%E9%9A%BE%E4%B8%8D%E7%AD%89%E5%BC%8F%E8%AF%81%E6%98%8E%E5%B7%B2%E7%9F%A5+%EF%BC%9Aa+%3E+0%2Cb+%3E+0%2Ca+%2B+b+%3D+1+.%E6%B1%82%E8%AF%81+%EF%BC%9A%EF%BC%88a+%2B+1%2Fa+%29%5E2+%2A%28+b+%2B+1%2Fb+%29%5E2%E2%89%A5+25%2F2+.%E6%8A%B1%E6%AD%89+%EF%BC%9A%E6%B1%82%E8%AF%81+%EF%BC%9A%EF%BC%88a+%2B+1%2Fa+%29%5E2+%2B+%28+b+%2B+1%2Fb+%29%5E2%E2%89%A5+25%2F2+.)
较难不等式证明已知 :a > 0,b > 0,a + b = 1 .求证 :(a + 1/a )^2 *( b + 1/b )^2≥ 25/2 .抱歉 :求证 :(a + 1/a )^2 + ( b + 1/b )^2≥ 25/2 .
较难不等式证明
已知 :a > 0,b > 0,a + b = 1 .求证 :(a + 1/a )^2 *( b + 1/b )^2≥ 25/2 .
抱歉 :求证 :(a + 1/a )^2 + ( b + 1/b )^2≥ 25/2 .
较难不等式证明已知 :a > 0,b > 0,a + b = 1 .求证 :(a + 1/a )^2 *( b + 1/b )^2≥ 25/2 .抱歉 :求证 :(a + 1/a )^2 + ( b + 1/b )^2≥ 25/2 .
(a + 1/a )^2 + ( b + 1/b )^2 =a^2+2+1/a^2+b^2+2+1/b^2 = (a + 1/a )^2 + ( b + 1/b )^2 =(a + (a+b)/a )^2 + ( b + (a+b)/b )^2 =(a+1+b/a)^2+(b+a/b+1)^2 =(a^2+1+b^2/a^2+2a+2b/a+2b)+(b^2+a^2/b^2+1+2a+2b+2a/b) =(a^2+b^2/a^2+2b/a+3)+(b^2+b^2/a^2+2a/b+3) =(a^2+b^2)+(b^2/a^2+a^2/b^2)+2(b/a+a/b)+6 ≥(a^2+b^2)+2+4+6 ≥(a^2+b^2)+12 ≥(a+b)^2/2+12 =1/2+12 =25/2
较难不等式证明已知 :a > 0,b > 0,a + b = 1 .求证 :(a + 1/a )^2 *( b + 1/b )^2≥ 25/2 .抱歉 :求证 :(a + 1/a )^2 + ( b + 1/b )^2≥ 25/2 .
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