Question

[Nguyễn Ngọc Thanh Nhi]

Bài 1: Tìm giá trị của x thỏa mãn hệ thức

a) (2x-1) (x\(^2\) - x +1) -2x\(^3\) + 3x\(^2\) = 2

b) (x+1) (x\(^2\) + 2x + 4 ) - x\(^3\) - 3x\(^2\) + 16 = 0

c) (x+1) (x+2) (x+5) - x\(^3\) - 8x\(^2\) = 27

Bài 2: Tính giá trị của đa thức

a) P(x) = x\(^7\) - 80x\(^6\) + 80x\(^5\) - 80x\(^4\) +.....+80x + 15 Với x=79

b) Q(x) = x\(^{14}\) - 10x\(^{13}\)+ 10x\(^{12}\) - 10x\(^{11}\)+ ..... + 10x\(^2\) - 10x + 10 Với x=9

Giúp mình với !!! Cảm ơn trước ạ !

Answer 1

[Trúc Giang]

Bài 2:

a) Vì x = 79 => x + 1 = 80

\(P\left(x\right)=x^7-80x^6+80x^5-80x^4+.....+80x+15\)

\(\Rightarrow P\left(x\right)=x^7-\left(x+1\right)x^6+\left(x+1\right)x^5-\left(x+1\right)x^4+.....+\left(x+1\right)x+15\)

\(=x^7-x^7-x^6+x^6+x^5-x^5-x^4+....+x^2+x+15\)

\(=x+15\)

Thay x = 79 vào đa thức ta được:

79 + 15 = 94

b) Vì x = 9 => x + 1 = 10

\(Q\left(x\right)=x^{14}-10x^{13}+10x^{12}-10x^{11}+.....+10x^2-10x+10\)

\(\Rightarrow Q\left(x\right)=x^{14}-\left(x+1\right)x^{13}+\left(x+1\right)x^{12}-\left(x+1\right)x^{11}+....+\left(x+1\right)x^2-\left(x+1\right)x+10\)

\(=x^{14}-x^{14}-x^{13}+x^{13}+x^{12}-x^{12}-x^{11}+....+x^3+x^2-x^2-x+10\)

\(=-x+10\)

\(=-9+10=1\)

P/s: Ko chắc nhé!

Answer 2

[Trúc Giang]

Bài 1:

a/ \(\left(2x-1\right)\left(x^2-x+1\right)-2x^3+3x^2=2\)

\(\Rightarrow2x\left(x^2-x+1\right)-1\left(x^2-x+1\right)-2x^3+3x^2=2\)

\(\Rightarrow2x^3-2x^2+2x-x^2+x-1-2x^3+3x^2=2\)

\(\Rightarrow3x-1=2\)

\(\Rightarrow3x=2+1=3\)

\(\Rightarrow x=3:3=1\)

b/ \(\left(x+1\right)\left(x^2+2x+4\right)-x^3-3x^2+16=0\)

\(\Rightarrow x\left(x^2+2x+4\right)+1\left(x^2+2x+4\right)-x^3-3x^2+16=0\)

\(\Rightarrow x^3+2x^2+4x+x^2+2x+4-x^3-3x^2+16=0\)

\(\Rightarrow6x+20=0\)

\(\Rightarrow6x=0-20=-20\)

\(\Rightarrow x=-\frac{20}{6}=-\frac{10}{3}\)

c/ \(\left(x+1\right)\left(x+2\right)\left(x+5\right)-x^3-8x^2=27\)

\(\Rightarrow\left[x\left(x+2\right)+1\left(x+2\right)\right]\left(x+5\right)-x^3-8x^2=27\)

\(\Rightarrow\left(x^2+2x+x+2\right)\left(x+5\right)-x^3-8x^2=27\)

\(\Rightarrow\left(x^2+3x+2\right)\left(x+5\right)-x^3-8x^2=27\)

\(\Rightarrow x^2\left(x+5\right)+3x\left(x+5\right)+2\left(x+5\right)-x^3-8x^2=27\)

\(\Rightarrow x^3+5x^2+3x^2+15x+2x+10-x^3-8x^2=27\)

\(\Rightarrow17x+10=27\)

\(\Rightarrow17x=27-10=17\)

\(\Rightarrow x=17:17=1\)