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Anonymous users2024-02-16a^3+b^3)-(a^2b+ab^2)
a^2(a-b)-b^2(a-b)
a-b)(a^2-b^2)
a-b)^2(a+b)
So when, a=b, or a+b=0, the two equations are equal.
When a is not equal to b, cut a+b is greater than 0 is, the former is larger, and the latter is larger.
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Anonymous users2024-02-15a^3-a^2*b+b^3-a*b^2>0a^2*(a-b)+b^2*(b-a)>0a^2*(a-b)-b^2*(a-b)>0a^2-b^2)*(a-b)>0
a+b)*(a-b)*(a-b)>0
a+b)*(a-b)^2>0
Because a≠b, (a-b) 2>0
If a, b are both positive.
then (a+b)*(a-b) 2>0
i.e. a 3 + b 3 > a 2 * b + a * b 2
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Anonymous users2024-02-14Solution: The size of the two is required, and the difference is used.
a³+b³-(a²b+ab²) =a³+b³-a²b-ab²a²(a-b) -b²(a-b)
a-b)(a²-b²)
a-b)²(a+b)
When a=b, a +b = a b+ab ;
a≠b, because (a-b) 0, so.
If a+b 0, then a +b a b+ab ;
If a+b 0, then a +b a b+ab ;
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Anonymous users2024-02-13because a 3+b 3=(a+b)(a 2+ab+b 2); And ah a b+ab = (a+b)ab
A +b is greater than or equal to 0, so when (a + b) > 0, then a 3 + b 3 is greater than or equal to a b + ab
If (a+b)<0, then a3+b3 is less than or equal to ab+ab
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Anonymous users2024-02-12Summary. If the power of 3 a is equal to the power b of 2, then we can do some reasoning to compare the magnitude of a to the power b of a and the power of a of b. First, we can simplify the problem by taking the logarithm.
We know that log(3 to the power a) = log(2 to the power b). Depending on the nature of the exponent, we can move a and b to the front of the exponent, i.e., a*log(3)=b*log(2). Now, let's compare the size of a to the power b and the power of b to the power a.
Suppose that the power of b of a is greater than the power of a of b, i.e., a b > b a. We can take the logarithm to simplify this inequality and get b*log(a)>a*log(b). Based on our previous derivation, we can write this inequality as b*log(3)>a*log(2).
Now, if we assume that both a and b are positive, we know that log(3) and log(2) are positive numbers less than 1. Therefore, the inequality b*log(3)>a*log(2) holds. This means that the power of b of a must be greater than the power of a of b.
To sum up, the power b of a must be greater than the power of a of b.
A power of 3 is equal to power b of 2, compare the magnitude of a to the power b of a to the power of a of b.
If the power of 3 a is equal to the power b of 2, then we can do some reasoning to compare the magnitude of a to the power b of a and the power of a of b. First, we can simplify the problem by taking the logarithm. We know that log(3 to the power a) = log(2 to the power b).
Depending on the nature of the exponent, we can move a and b to the front of the exponent, i.e., a*log(3)=b*log(2). Now, let's compare the size of a to the power b and the power of b to the power a. Suppose that the power of b of a is greater than the power of a of b, i.e., a b > b a.
We can take the logarithm to simplify this inequality and get b*log(a)>a*log(b). Based on our previous derivation, we can write this inequality as b*log(3)>a*log(2). Now, if we assume that both a and b are positive, we know that log(3) and log(2) are positive numbers less than 1.
Therefore, the unequal b*log(3)>a*log(2) holds. This means that the power of b of a must be greater than the power of a of b. To sum up, A's B power must be more than B's A defeat to Kai's.
You've done a great job! Can you elaborate on that?
If the power of 3 to the power of a is equal to the power of 2 to the power of b, then we can conclude that the power b of the disturbance a must be greater than the power of b of b.
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Anonymous users2024-02-11A 15=3 5=243 B 15=4 3=64 A 15>B 15 A>0 B>0 A>B Hello classmates, if the problem has been solved, remember to hold the corner only on the upper right Yours is the affirmation of the reprieve
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Anonymous users2024-02-10a^2=2a^2)^3=a^6=2^3=8b^3=3b^3)^2=b^6=3^2=9b^6>a^6
When both file A and B are greater than Zheng San's 0, B > A
When both a and b are less than 0, b
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Anonymous users2024-02-09a^3+b^3=（a+b）（a^2+b^2-ab）（1）,ab^2+a^2b=ab（a+b）,（2）
1) Formula - (2) has (a+b) (a 2+b 2-ab-ab) Yuxiao, because a + b 0, and has a 2+b 2-ab-ab=(a-b) 2 0, so (a + b) and friends (call to dismantle a 2+b 2-ab-ab) 0, so there is a 3+b 3 ab 2+a 2
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Anonymous users2024-02-08The topic is: set a>b>0, try to compare the size of a a*b b and b a*a b.
Since A> traces of Weisen Mountain then B, so A-B>0, then has:
a^(a-b)>b^(a-b)
a^a/a^b>b^a/b^b
Get: a a*b b>b a*a b
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