Question

数学题，看图，求解

c等于什么？

Answer 1

(1)-4,8,4
(2)(x+1/2)^2+y^2=65/4
(3)设圆方程为(x-a)^2+(y-b)^2=r^2
(5-a)^2+(2-b)^2=r^2
(3-a)^2+(2-b)^2=r^2
2a-b-3=0
a=4,b=2,r=1
(x-4)^2+(y-2)^2=1
(4)设圆方程为(x-a)^2+(y-b)^2=r^2
a-3b=0
a=r或-a=r
a^2-7=(a-b)^2/2
a=3，b=1，r=3
或a=-3，b=-1，r=3
(x-3)^2+(y-1)^2=9或(x+3)^2+(y+1)^2=9

Answer 2

2^a = 5^b = 20^c
alg2 = clg20 , c = alg2/lg20 = alg2/(1+lg2), lg2 = c/(a-c)
同理 c = blg5/lg20 = b(1-lg2)/(1+lg2)
= b[1-c/(a-c)]/[1+c/(a-c)] = b(a-2c)/a
ac = ab - 2bc, c = ab/(a+2b)

Answer 3

2^a=5^b=20^c=t
c=log20(t)=log20(2^a)=log20(5^b)

追问

一次性把a和b都合在一起，怎么写？

追答

20^(ab)
=2^(ab)*2^(ab)*5^(ab)
=2^(2ab)*5^(ab)
=(2^a)^(2b)*(5^b)^a
=t^(2b)* t^a
=t^(2b+a)
把t=20^c代入得
20^(ab)=20^c(2b+a)
所以 ab=c(2b+a)
c=ab/(2b+a)