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If a is a positive real number, then a + 1 / A is greater than or equal to 2
Because a > 0, according to the basic inequality: a + 1 / a > = 2
If you haven't learned: write like this: a + 1 / a = a + 1 / A-2 + 2 = (√ A-1 / √ a) ^ 2 + 2 ≥ 2
It is known that a and B are positive real numbers, and a is not equal to B. prove a ^ 3 + B ^ 3 > (a ^ 2) B + a (b ^ 2)
It is proved by the analysis method of senior two
It is proved that (a + b) (A & sup2; - AB + B & sup2;) > AB (a + b)
∵a＞0,b＞0
We only need to prove a & sup2; - AB + B & sup2; > ab
That is, a & sup2; - 2Ab + B & sup2; > 0 holds
∵a≠b,∴a-b≠0
(a-b) & sup2; > 0 holds
Get proof
It is known that a is a real number. It is proved by analysis that (1 / a) + 1 / (1-A) is greater than or equal to 4
If 0 = 4
0
Let a and B be real numbers, and write the necessary and sufficient condition for ab > 0
It is a > 0, b > 0 or a > 0
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