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Let a and B be positive numbers, and a + B = 1, then the minimum value of 12a + 1b is______ ．
∵ a, B are positive numbers, and a + B = 1, ∵ 12a + 1b = (12a + 1b) (a + b) = 12 + 1 + B2A + ab ≥ 32 + 212 = 32 + 2, if and only if B2A = AB, i.e. B = 2A, take the equal sign. So the answer is 2 + 32
Given AB > 0,2a + B = 1, find the minimum value of 1 / A + 2 / b
1/a+2/b
=(2a+b)/a+2(2a+b)/b
=2+b/a+4a/b+2
=4+b/a+4a/b>=4+2√4=8
The equal sign holds if and only if B = 2A, a = 1 / 4, B = 1 / 2
The minimum is 8
Given a > 1, a ^ (LGB) = 10, what is the minimum value of LG (AB)
a^(lgb)=10
loga(10)=lgb
1/log10(a)=lgb
1/lga=lgb
lga*lgb=1
√(lga*lgb)
The distance from a point on the number axis to - 3 is 8, then the number represented by this point on the number axis is 8____
+5 or - 11
Given that the absolute value of the number a is three times that of the number B, and the distance between the two points of the number a and B is 8 on the number axis, find the two numbers a and B (please tell me the method and answer)
［a］＝3［b］
There are two cases
（1）
A-B = ± 8
＝＞a＝12,b＝4；a＝-12,b＝－4.
(2) A, B different sign
［a］＋［b］＝8
A = - 6, B = 2; a = 6, B = - 2
On the number axis, the distance between a and B is 18. The absolute value of B is three times of that of A. find the numbers represented by a and B respectively
a-b=18
a=3b
The solution is a = 27, B = 9
a-b=18
a=-3b
The solution is a = 13.5, B = - 4.5
a-b=-18
a=3b
The solution is a = - 27 and B = - 9
a-b=-18
a=-3b
The solution is a = - 13.5, B = 4.5
On the number axis, if point a and point B are two opposite numbers, and the distance between the two points is 12.8, then the two points represent
6.4 - 6.4 directly divide 12.8 by 2 and sign it
If M and N represent a pair of opposite numbers on the number axis, and the distance between the two points is 4.8
How many are m and N
M is 2.4, n is - 2.4
It is known that there are two points m and N on the number axis. They represent two numbers m and n which are opposite to each other (where m > n), and the distance between M and N is 10
10/2=5
m>n
m=5,n=-5
Given that the two numbers represented by point m and point n on the number axis are opposite to each other, and whether the distance between the two points is. 2 unit length, find the
The number represented by these two points
+2.5 and - 2.5
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