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Giải hệ 3 ẩn ba pt =>a,b,c =>đề đúng =>a,b,c phải nguyên=>đpcm
\(f\left(5\right)-f\left(4\right)=\left(125a+25b+5c+d\right)-\left(64a+16b+4c+d\right)=61a+9b+c=2019\)
\(f\left(7\right)-f\left(2\right)=\left(343a+49b+7c+d\right)-\left(8a+4b+2c+d\right)=335a+45b+5c=5.\left(61a+9b+c\right)+30a=2019+30a⋮3\)
\(\Rightarrowđpcm\)
f(5)=125a+25b+5c+d
f(4)=64a+16b+4c+d
=>f(5)-f(4)=(125a+25b+5c+d)-(64a+16b+4c+d)
=125a+25b+5c+d-64a-16b-4c-d
=61a+9b+c=2019
f(7)=343a+49b+7c+d
f(2)=8a+4b+2c+d
f(7)-f(2)=(343a+49b+7c+d)-(8a+4b+2c+d)
=343a+49b+7c+d-8a-4b-2c-d
=335a+45b+5c
=5(67a+9b+c)
=5(6a+1019) chia hết cho 5
Vậy f(7)-f(2) là hợp số (đpcm)
Ta có : \(f\left(5\right)-f\left(4\right)=2019\Leftrightarrow\left(125a+25b+5c+d\right)-\left(64a+16b+4c+d\right)=2019\)
\(\Leftrightarrow61a+9b+c=2019\left(1\right)\)
Lại có : \(f\left(7\right)-f\left(2\right)=\left(345a+49b+7c+d\right)-\left(8a+4b+2c+d\right)\)
\(=335a+45b+5c=305a+45b+5c+30a=5\left(61a+9b+c\right)+30a\)
\(=2012+30a=2\left(1006+15a\right)⋮2\left(2\right)\)
\(\Rightarrowđpcm\)
cho f(x) = ax3 + bx2+c+d (a,b,c,d thuoc z) va thoa man b= 3a+c
cmr: f(1) , f(-2) la binh phuong mot so nguyen
cau hoi vay ai tra loi giup minh voi
\(f\left(1\right)=a.1^3+b.1^2+c.1+d\)
\(=a+b+c+d\)
\(=a+3a+c+c+d\)
\(=4a+2c+d\)
\(f\left(-2\right)=a.\left(-2\right)^3+b.\left(-2\right)^2+c.\left(-2\right)+d\)
\(=-8a+4b-2c+d\)
\(=-8a+4\left(3a+c\right)-2c+d\)
\(=-8a+12a+4c-2c+d\)
\(=4a+2c+d\)
\(\text{Có : }f\left(1\right).f\left(-2\right)=\left(4a+2c+d\right).\left(4a+2c+d\right)\)
\(=\left(4a+2c+d\right)^2\)
\(\text{Vậy ..................................(đpcm)}\)
Ta có:
\(f\left(5\right)=125a+25b+5c+d\)
\(f\left(4\right)=64a+16b+4c+d\)
\(f\left(7\right)=343a+49b+7c+d\)
\(f\left(2\right)=8a+4b+2c+d\)
Xét:
\(f\left(5\right)-f\left(4\right)=125a+25b+5c+d-64a-16b-4c-d\)
\(=61a+9b+c=2019\)
Khi đó:
\(f\left(7\right)-f\left(2\right)=343a+49b+7c+d-8a-4b-2c-d\)
\(=335a+45b+5c=5\left(61a+9b+c\right)+30=5\cdot2019+30⋮5\)
Vậy ta có đpcm
Đề sai
f(5) = f(5) nên f(5) - f(5) = 0
bạn xem lại đề có phải f(5)-f(4) không?
hok tốt
kt