cho 5a-b+2c/c=5b-2c+a/a=5c-2a+b/b(a,b,c>0).Tinh gtbt A=(4b+2a)*(4c+2b)*(4a+2c)/(5a-2b)*(5b-2c)*(5c-2a)
a/b+c+d=b/a+c+d=c/b+a+d=d/c+b+a
P=2a+5b/3c+4d-2b+5c/3d+4a-2c+5d/3a+4b+2d+5a/3c+4b
Cho a+b+c+d ≠ 0 thỏa mãn:
\(\dfrac{a}{b+c+d}=\dfrac{b}{a+c+d}=\dfrac{c}{b+a+d}=\dfrac{d}{c+b+a}\)
Tính P = \(\dfrac{2a+5b}{3c+4d}+\dfrac{2b+5c}{3d+4a}+\dfrac{2c+5d}{3a+4b}+\dfrac{2d+5a}{3c+4b}\)
Cho a+b+c+d ≠ 0 và \(\dfrac{a}{b+c+d}=\dfrac{b}{a+c+d}=\dfrac{c}{b+a+d}=\dfrac{d}{c+b+a}\)
Tính giá trị biểu thức:
P = \(\dfrac{2a+5b}{3c+4d}-\dfrac{2b+5c}{3d+4a}+\dfrac{2c+5d}{3a+4b}+\dfrac{2d+5a}{3c+4b}\)
cho tỷ lệ thức a/b=c/d. chứng minh:
a, 2a+5b/3a-4b=2c+5d/3c-4d
b. 3a+7b/5a-7b=3c+7d/5c-7d
d. 4a+9b/4a-7b=4c+9d/4c-7d
giúp mình với ạ
Thu gọn biểu thức:
a) 2.( a-3b+5b) + (-3a-7c+5c) -4b b)7.(-a-2b+c)+3.(-2c-6b+a)
c)2.(-3c-6b+7b)-4.(2a-3b+8c) d) -3.(2a+3b-4c)+7.(-2c+8a-2c)+20a+2a+24b
e)-(5a-6b+c)+3.(-2c-6b+a)
1.cho a^2-b^2=4c^2.CM: (5a-3b+8c)(5a-3b-8c)=(3a-5b)^2
2.cho a^2+b^2+c^2=2017. Tính M=(2a+2b-c)^2+(2b+2c-a)^2+(2c+2a-b)^2
a, Vì \(a^2-b^2=4c^2\Rightarrow16a^2-16b^2=64c^2\) (1)
Ta có:\(\left(5a-3b+8c\right)\left(5a-3b-8c\right)=\left(5a-3b\right)^2-\left(8c\right)^2\)
\(=25a^2-30ab+9b^2-64c^2\) (2)
Thay (1) vào (2) ta được
\(\left(5a-3b+8c\right)\left(5a-3b-8c\right)=25a^2-30ab+9b^2-16a^2+16b^2\)
\(=9a^2-30ab+25b^2=\left(3a-5b\right)^2\)
=> đpcm
b, \(M=\left(2a+2b-c\right)^2+\left(2b+2c-a\right)^2+\left(2c+2b-b\right)^2\)
\(=4a^2+4b^2+c^2+4b^2+4c^2+a^2+4c^2+4a^2+b^2\)
\(+8ab-4ac-4bc+8bc-4ab-4ac+8ac-4bc-4ab\)
\(=9.\left(a^2+b^2+c^2\right)=9.2017=18153\)
Vậy M=18153
\(\dfrac{5a+3b}{3a+b+2c}\)+\(\dfrac{5b+3c}{3b+c+2a}\)+\(\dfrac{5c+3a}{3c+a+2b}\)\(\ge4\) a,b,c là độ 3 cạnh tam giác
Thu gọn biểu thức sau
a) 3a + 4b - 5c - 2a - 3b + 5c
b) 7a + 3b - 4c - 3a+ 2b - 2c - 4a + b - 2c
a) 3a + 4b - 5c - 2a - 3b + 5c
= ( 3a - 2a ) + ( 4b - 3b ) - ( 5c - 5c )
= a + b
b) 7a + 3b - 4c - 3a + 2b - 2c - 4a + b - 2c
= ( 7a - 3a - 4a ) + ( 3b + 2b + b ) - ( 4c + 2c + 2c )
= 6b - 8c
a) 3a + 4b - 5c - 2a - 3b + 5c
= (3a - 2a) + (4b - 3b) - (5c - 5c)
= a + b - 0 = a + b
b) 7a + 3b - 4c - 3a + 2b - 2c - 4a + b - 2c
= (7a - 3a - 4a) + (3b + 2b + b) - ( 4c + 2c + 2c)
= 0 + 6b - 8c = 6b - 8c
a)
3a + 4b - 5c - 2a - 3b + 5c
=( 3a - 2a ) + ( 4b - 3b ) + ( -5c + 5c )
= a + b
b)
7a + 3b - 4c - 3a + 2b - 2c - 4a + b - 2c
=( 7a - 3a - 4a ) + ( 3b + 2b + b ) + ( -4c - 2c - 2c )
= 6b + (-8c)
Cho a, b, c > 0:
CMR: \(\frac{1}{5a+b}+\frac{1}{5b+c}+\frac{1}{5c+a}\ge\frac{1}{a+3b+2c}+\frac{1}{b+3c+2a}+\frac{1}{c+3a+2b}\)
Xin ngoại lệ ạ ( Ko liên quan đến câu hỏi)