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A= x^3(x-17) + 17x(x-1) +20
=16^3.(-1) +17.16.15+20 = (16+1)(16-1).16 -16^3+20
= (16^2-1).16 -16^3+20 = 16^3-16+16^3+20=4
B= x^4(x-15) + 16x^2(x-1) + 13x . (-x+1)
= -14^4 +16.14^2.13 + 13.14.(-13)= -14^4 +(15+1).14^2.13 -13^2.14
= -14^4 +15.14^2.13 + 14^2.13 - 13^2.14= -14^4 +(14+1).14^2.(14-1) -13^2.14
= -14^4 +(14^2-1).14^2 +13.14 = -14^4 +14^4 -14^2 +13.14= 14(13-14) = -14
\(A=x^4-17x^3+17x^2-17x+20\)
\(=x^4-\left(x+1\right)x^3+\left(x+1\right)x^2-\left(x+1\right)x+x+4\)
\(=x^4-x^4-x^3+x^3+x^2-x^2-x+x+4\)
\(=4\)
x=16 nên x+1=17
\(A=x^4-x^2\left(x+1\right)-x\left(x+1\right)+x+4\)
\(=x^4-x^3-x^2-x^2-x+x+4\)
\(=x^4-x^3-2x^2+4\)
\(=16^4-16^3+2\cdot16^2+4=61956\)
`G(x)+H(x)=(21x^2+1+17x)+(-2+6x^3-12x^2-8)`
`=21x^2+1+17x-2+6x^3-12x^2-8`
`= 6x^3+(21x^2-12x^2)+17x+(1-2-8)`
`= 6x^3+9x^2+17x-9`
`G(x)-H(x)=(21x^2+1+17x)-(-2+6x^3-12x^2-8)`
`= 21x^2+1+17x+2-6x^3+12x^2+8`
`= -6x^3+(21x^2+12x^2)+17x+(1+2+8)`
`= -6x^3+33x^2+17x+11`
`----`
`M(x)+N(x)=(7x^5 + 1 + 17x^4 - 2)+(6x^4 - 12x^2 - 23x^4 + x)`
`= 7x^5 + 1 + 17x^4 - 2+6x^4 - 12x^2 - 23x^4 + x`
`= 7x^5+(17x^4+6x^4-23x^4)-12x^2+x+(1-2)`
`= 7x^5-12x^2+x-1`
`M(x)-N(x)=(7x^5 + 1 + 17x^4 - 2)-(6x^4 - 12x^2 - 23x^4 + x)`
`= 7x^5 + 1 + 17x^4 - 2-6x^4 + 12x^2 + 23x^4 - x`
`= 7x^5+(17x^4-6x^4+23x^4)+12x^2-x+(1-2)`
`= 7x^5+34x^4+12x^2-x-1`
Mình đã trl rồi nha!
(https://hoc24.vn/cau-hoi/tinh-tong-avf-hieu-cac-da-thuc-saugx-21x2-1-17x-va-hx-2-6x3-12x2-8mx-7x5-1-17x4-2-va-nx-6x4-12x2-23x4-x.7858748287383)
thay x = 16, ta có :
16^4-17*16^3+17*16^2-17*16+20
=16^4-17*(16^3-16^2+16)+20
=65536-17*3856+20
=65536-65552+20
=4
theo bài ra ta có:\
\(M=x^4-17x^3+17x^2-17x+20\\ \Rightarrow M=x^4-\left(16x^3+x^3\right)+\left(16x^2+x^2\right)-\left(16x+x\right)+20\\ \Rightarrow M=x^4-16x^3-x^3+16x^2+x^2-16x-x+20\left(1\right)\) thay x = 16 vào 1 ta có:
\(M=x^4-x.x^3-x^3+x.x^2+x^2-x.x-x+20\)
\(\Rightarrow M=x^4-x^4-x^3+x^3+x^2-x^2-x+20\\ \Rightarrow M=-x+20\\ \Rightarrow M=-16+20\\ \Rightarrow M=4\)
vậy M = 4