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Given that a & # 178; + B & # 178; - A + 4B + 17 / 4 = 0, find the value of a and B
It is known that a & # 178; + B & # 178; - A + 4B + 17 / 4 = 0
a²-a+1/4+b²+4b+4=0
(a-1/2)²+(b+2)²=0
(a-1/2)=0 (b+2)=0
a=1/2 b=-2
The greatest common divisor of a and B is 12, the least common multiple is 180, the number a is 60, and what is the number B?
Greatest common divisor × least common multiple = a × B
So B = 36
Given that a, B and C are positive numbers, and the square of a + B + C = 14, find the minimum value of a + 2B + 3C
C is the smallest positive number, B is the second, a is the largest, 1.2.3
3+4+3=10
A = 3, B = 2, C = 1, 3 + 4 + 3 = 10
a+2b+3c>=sqrt(14)
The greatest common factor of two numbers is 12, and the least common multiple is 60. The product of these two numbers is___ .
12 = 2 × 2 × 3, 60 = 2 × 2 × 3 × 5, one number is: 2 × 3 × 3 = 12, the other number is: 2 × 3 × 5 × 2 = 60, the product of these two numbers is: 12 × 60 = 720
It is known that a + 2B + 3C = 6
ditto
The least common multiple of two numbers is 240, and the greatest common divisor is 12. It is known that one number is 60, and the other is 60______ .
240 = 12 × 20, 60 = 12 × 5, because: 20 = 5 × 4, so the other number is 12 × 4 = 48
14 (the square of a plus the square of B plus the square of C) is derived from the square of (a plus 2B plus 3C), then a: B: C is equal to
14（a*2+b*2+c*2）=(a+2b+3c)*2
14a*2+14b*2+14c*2 = a*2+4b*2+9c*2+6ac+12bc
13a*2+10b*2+5c*2-4ab-6ac-12bc = 0
(2a-b)*2+(3a-c)*2+(3b-2c)*2 = 0
Because (2a-b) * 2, (3a-c) * 2, (3b-2c) * 2 is greater than or equal to 0, the sum is equal to 0
So 2a-b = 0 3a-c = 0 3b-2c = 0
The solution is a: B: C = 1:2:3
Column: * 2 is square
If the greatest common divisor of two numbers is 3 and the least common multiple is 60, then the two numbers are（
12 and 15
The square of (a-2b + 3C)
(a-2b+3c)^2
=[(a-2b)+3c]^2
=a^2+4b^2+9c^2-4ab+6ac+12bc
Two two digit numbers, their greatest common divisor is 9, the least common multiple is 360, these two two digit numbers are______ And______ .
360 △ 9 = 40, 40 means that the product of two coprime numbers is 40 = 5 × 8, so the two two digits are: 5 × 9 = 45, 8 × 9 = 72; so the answer is: 45, 72
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