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Ta có: x=79
nên x+1=80
\(P\left(x\right)=-x^6\left(x+1\right)+x^5\left(x+1\right)-x^4\left(x+1\right)+...+x\left(x+1\right)+15\)
\(=-x^7+x+15\)
\(=-79^7+94\)
Lời giải:
\(P=-80(x^6-x^5+x^4-x^3+x^2-x+1)+95\)
\(=-(x+1)(x^6-x^5+x^4-x^3+x^2-x+1)+95=-(x^7+1)+95\)
\(=-79^7+94\)
x=79
nên x+1=80
\(P\left(x\right)=-80x^6+80x^5-80x^4+...+80x+15\)
\(=-x^6\left(x+1\right)+x^5\left(x+1\right)-x^4\left(x+1\right)+...+x\left(x+1\right)+15\)
\(=-x^7-x^6+x^6+x^5-x^5-x^4+...+x^2+x+15\)
\(=-x^7+x+15\)
\(=-79^7+79+15\)
\(=-79^7+94\)
\(x=79\Leftrightarrow x+1=80\\ \Leftrightarrow P\left(x\right)=-\left(x+1\right)x^6+\left(x+1\right)x^5-\left(x+1\right)x^4+...+\left(x+1\right)x+15\\ P\left(x\right)=-x^7-x^6+x^6+x^5-x^5-x^4+...+x^2+x+15\\ P\left(x\right)=-x^7+x+15=-79^7+94\)
Vì \(x=79\Rightarrow80=x+1\)
\(\Rightarrow A\left(x\right)=x^7-\left(x+1\right)x^6+\left(x+1\right)x^5-\left(x+1\right)x^4+...+\left(x+1\right)x+15\)
\(\Rightarrow A\left(x\right)=x^7-x^7-x^6+x^6+x^5-x^5-x^4+...+x^2+x+15\)
\(\Rightarrow A\left(x\right)=x+15=79+15=94\)
Thay x+1=80 ta đc:
\(P\left(x\right)=x^7-\left(x+1\right)x^6+\left(x+1\right)x^5-\left(x+1\right)x^4+...+\left(x+1\right)x+15\)
\(=x^7-x^7-x^6+x^6+x^5+...+x^2+x+15\)
\(79+15=94\)
\(Ta \) \(có \) \(:\)
\(x = 79 \)\(\Rightarrow\)\(x + 1 = 80\)
\(Thay \) \(x + 1 = 80 \) \(vào \) \(P(x)\) \(ta\) \(được :\)
\(P ( x ) = x ^7 - ( x + 1 )x ^6 + ( x + 1 )x^5\)\(- ( x + 1 )x ^4\)\(+ ...+ ( x + 1 )x + 15\)
\(P ( x ) = x ^7 - x ^7- x^6 + x^6 + x^5 - x^ 5\)\(- x ^4 + x ^4 + ... - x^ 2 + x ^2 + x + 15\)
\(P ( x ) = x + 15\)
\(Thay x = 79 vào P ( x ) ta được :\)
\(P ( x ) = 79 + 15 = 94\)
Ta có : x = 79
=> x + 1 = 80
Thay vào A ta có : A = x7 - (x + 1)x6 + (x + 1)x5 - (x + 1).x4 + (x + 1).x3 - (x + 1)x2 + (x + 1)x + 15
=> A = x7 - x7 - x6 + x6 + x5 - x5 - x4 + x4 + x3 - x3 - x2 + x2 + x + 15
=> A = x + 15
=> A = 79 + 15
=> A = 94
Ta có: x=79 => x+1=80
\(\Rightarrow P\left(x\right)=x^7-80x^6+80x^5-80x^4+...+80x+15\)
\(=x^7-\left(x+1\right)x^6+\left(x+1\right)x^5-\left(x+1\right)x^4+...+\left(x+1\right)x+15\)
\(=x^7-x^7-x^6+x^6+x^5-x^5-x^4+...+x^2+x+15\)
\(=x+15=80+15=95\)
Vậy P(x)=95 tại x=80
P/s: mk sửa đề r nha
x = 79 => x+1 = 80
Thay x+1 = 80 vào P(x)=x7- 80x6 + 80x5 - 80 x4 + ... + 80x + 15, có:
P(x)=x7- (x+1)x6 + (x+1)x5 - (x+1) x4 + ... + (x+1)x + 15
P(x) = \(x^7-x^7-x^6+x^6+x^5-x^5-x^4+...+x^2+x+15\)
P(x) = \(x+15\)
Thay x = 79 vào P(x) = x+15; cs:
P(x) = 79 + 15 = 94
\(x=79\Rightarrow80=x+1\)
\(B=x^7-\left(x+1\right)x^6+\left(x+1\right)x^5-\left(x+1\right)^4+...+\left(x+1\right)x+15\)
\(=x^7-x^7+...+x+15=79+15=94\)