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\(\left(x-8\right)^2+36=x^2-16x+64+36=x^2-16x+100>0\)
xem lại đề
\(a,x^2-x-6\)
\(=x^2+2x-3x-6\)
\(=x\left(x+2\right)-3\left(x+2\right)\)
\(=\left(x+2\right)\left(x-3\right)\)
\(b,x^4+4x^2-5\)
\(=x^4-x^2+5x^2-5\)
\(=x^2\left(x^2-1\right)+5\left(x^2-1\right)\)
\(=\left(x^2-1\right)\left(x^2+5\right)\)
\(=\left(x-1\right)\left(x+1\right)\left(x^2+5\right)\)
\(c,x^3-19x-30\)
\(=x^3-25x+6x-30\)
\(=x\left(x^2-25\right)+6\left(x-5\right)\)
\(=x\left(x-5\right)\left(x+5\right)+6\left(x-5\right)\)
\(=\left(x-5\right)\left(x^2+5x+6\right)\)
\(=\left(x-5\right)\left(x^2+2x+3x+6\right)\)
\(=\left(x-5\right)\left[x\left(x+2\right)+3\left(x+2\right)\right]\)
\(=\left(x-5\right)\left(x+3\right)\left(x+2\right)\)
1.
a.x2-x-6=(x2-3x)+(2x-6)=(x-3)(x+2)
b.x4+4x2-5=(x4+4x2+4)-9=(x2+2)2-32=(x2+2-3)(x2+2+3)=(x2-1)(x2+5)
2.
a.A=ab(a-b)+bc(b-c)+ca(c-a)=ab(a-b)+bc(b-c)-ca(a-c)=ab(a-b)+bc(b-c)-ca(a-b+b-c)=(ab-ca)(a-b)-(ca-bc)(b-c)
=(a-c)(a-b)(b-c)
b.Tách tương tự câu a
c.C=(a+b+c)3-a3-b3-c3=a3+b3+c3+3(a+b)(b+c)(c+a)-a3-b3-c3=3(a+b)(b+c)(c+a)
a) Mình không hiểu cho lắm x^2y^2 là thế nào nhỉ :v
b) x^3 - 3x^2 + 3x - 1 = (x - 1)^3 = (101-1)^3 = 100^3 = 10000
c) x^3 + 9x^2 + 27x + 27 = (x +3)^3 = (97+3)^3 = 100^3 = 10000
a) \(x^2-x-6\)
\(=x^2-3x+2x-6\)
\(=\left(x^2-3x\right)+\left(2x-6\right)\)
\(=x.\left(x-3\right)+2.\left(x-3\right)\)
\(=\left(x-3\right).\left(x+2\right)\)
\(a^3-7a=6\)
\(=a^3+a^2-a^2-a-6a-6\)
\(=a^2\left(a+1\right)-a\left(a+1\right)-6\left(a+1\right)\)
\(=\left(a+1\right)\left(a^2-a-6\right)\)
\(=\left(a+1\right)\left(a^2-3a+2a-6\right)\)
\(=\left(a+1\right).\left[a\left(a-3\right)+2\left(a-3\right)\right]\)
\(=\left(a+1\right)\left(a-3\right)\left(a+2\right)\)
a2(b + c) + b2(c + a) + c2(a + b) + 2abc
=\(a^2b+a^2c+b^2c+b^2a+ca^2+cb^2+2abc\)
\(=\left(a^2b+ab^2\right)+\left(a^2c+ac^2\right)+\left(b^2c+bc^2\right)+2abc\)
\(=ab\left(a+b\right)+ac\left(a+b\right)+bc\left(a+b\right)+2abc\)
\(=\left(a+b\right)\left(ab+ac+bc+c^2\right)\)
\(=\left(a+b\right)\left(ab+bc\right)+\left(c^2+ac\right)\)
\(=\left(a+b\right)\left(b+c\right)\left(a+c\right)\)
\(A=\left(100-99\right)\left(100+99\right)+\left(99-98\right)\left(98+97\right)+...+\left(2-1\right)\left(2+1\right)\\ A=100+99+99+98+...+2+1\\ A=\left(100+1\right)\left(100-1+1\right):2=5050\)
\(B=\left(2-1\right)\left(2+1\right)\left(2^2+1\right)\left(2^4+1\right)...\left(2^{64}+1\right)+1\\ B=\left(2^1-1\right)\left(2^2+1\right)\left(2^4+1\right)\left(2^8+1\right)...\left(2^{64}+1\right)+1\\ B=\left(2^4-1\right)\left(2^4+1\right)\left(2^8+1\right)...\left(2^{64}+1\right)+1\\ B=\left(2^8-1\right)\left(2^8+1\right)\left(2^{16}+1\right)...\left(2^{64}+1\right)+1\\ B=\left(2^{16}-1\right)\left(2^{16}+1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)+1\\ B=\left(2^{32}-1\right)\left(2^{32}+1\right)\left(2^{64}+1\right)+1\\ B=\left(2^{64}-1\right)\left(2^{64}+1\right)+1=2^{128}-1+1=2^{128}\)
\(C=a^2+b^2+c^2+2ab+2bc+2ac+a^2+b^2+c^2+2ab-2ac-2bc-2a^2-4ab-2b^2\\ C=2c^2\)
Cũa mị:>>>
Tham khảo ạ !!!
A = 1002 - 992 + 982 - 972 + ...... + 22 - 12
= ( 100 - 99 ) ( 100 + 99 ) + ( 98 - 97 ) ( 98 + 97 ) + ......... + ( 2 - 1 ) ( 2 + 1 )
= 1 + 2 + 3 + ......... + 99 + 100
= ( 100 + 1 ) . 100 : 2 = 5050
B = 3 ( 22 + 1 ) ( 24 + 1 ) ... ( 264 + 1 ) + 12
= ( 22 - 1 ) ( 22 + 1 ) ( 24 + 1 ) ... ( 264 + 1 ) + 1
= ( 24 - 1 ) ( 24 + 1 ) ... ( 264 + 1 ) + 1
= ( 28 - 1 ) ( 28 + 1 ) ... ( 264 + 1 ) + 1
= ( 216 - 1 ) ( 216 + 1 ) ... ( 264 + 1 ) + 1
= ( 232 - 1 ) ( 232 + 1 ) ( 264 + 1 ) + 1
= ( 264 - 1 ) ( 264 + 1 ) + 1
= 2128 - 1 + 1
= 2128
C = ( a + b + c )2 + ( a + b - c )2 - 2 ( a + b )2
= a2 + b2 + c2 + 2ab + 2bc + 2ca + a2 + ab - ac + ab + b2 - bc - ac - bc + c2 - 2 ( a2 + 2ab + b2 )
= a2 + b2 + c2 + 2ab + 2bc + 2ca + a2 + ab - ac + ab + b2 - bc - ac - bc + c2 - 2a2 - 4ab - 2b2
= 2c2
a) \(A=x^2-6x+9-9y^2\)
\(=\left(x-3\right)^2-\left(3y\right)^2\)
\(=\left(x-3-3y\right)\left(x-3+3y\right)\)
b) \(B=x^3-3x^2+3x-1+2\left(x^2-1\right)\)
\(=\left(x-1\right)^3+\left(2x+2\right)\left(x-1\right)\)
\(=\left(x-1\right)\left[\left(x-1\right)^2+2x+2\right]\)
\(=\left(x-1\right).\left(x^2+3\right)\)
a, \(A=\left(x-3\right)^2-9y^2=\left(x-3-3y\right)\left(x-3+3y\right)\)
b, \(B=\left(x-1\right)^3+2\left(x-1\right)\left(x+1\right)=\left(x-1\right)\left[\left(x-1\right)^2+2\left(x+1\right)\right]\)
\(=\left(x-1\right)\left(x^2-2x+1+2x+2\right)=\left(x-1\right)\left(x^2+3\right)\)