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a,
=\(\left(a^2\right)^2-\left(2b\right)^2\)
=\(\left(a^2-2b\right)\left(a^2+2b\right)\)
= \(\left(\left(a-\sqrt{2b}\right)\left(a+\sqrt{2b}\right)\right)\left(a^2+2b\right)\)
c,
=\(4x^4+20x^2+25\)
=\(\left(2x^2\right)^2+2.2x^2.5+5^2\)
=\(\left(2x^2+5\right)^2\)
d,
=\(8x^6-27y^3\)
= \(\left(2x^2\right)^3-\left(3y\right)^3\)
= \(\left(2x^2-3y\right)\left(4x^4+6x^2y+9y^2\right)\)
Câu b đề ghi ko rõ lắm
a) \(6x^2-11xy+3y^2=6x^2-2xy-9xy+3y^2=2x.\left(3x-y\right)-3y.\left(3x-y\right)\)
= \(\left(3x-y\right).\left(2x-3y\right)\)
b) PP: dùng hệ số bất định
ta có: x^4 -3x^3+6x^2-5x+3=(x^2+ax-1)(x^2 +bx-3) (*)
=x^4 +bx^3-3x^2+ax^3 +(a+b)x^2 -3ax -x^2-bx+3
=x^4 +(b+a)x^3 +(a+b-3-1)x^2 -(3a+b)x +3
=> a+b=-3
a+b-4=6
3a+b=5
<=> a=7/2 ;b=13/2 thay vào (*) ta đc: x^4 -3x^3+6x^2-5x+3=(x^2+\(\frac{7}{2}\).x -1)(x^2 +\(\frac{13}{2}\).x -3)
Hay x^4 -3x^3+6x^2-5x+3= \(\frac{1}{4}.\left(2x^2+7x-2\right)\left(2x^2+13-6\right)\)
\(ab\left(a-b\right)+bc\left(b-c\right)+ca\left(c-a\right)\)
\(=ab\left(a-b\right)+bc\left(b-c\right)-ca\left(a-c\right)\)
\(=ab\left(a-b\right)+bc\left(b-c\right)-ca\left(a-b+b-c\right)\)
\(=ab\left(a-b\right)+bc\left(b-c\right)-ca\left(a-b\right)-ca\left(b-c\right)\)
\(=\left(a-b\right)\left(ab-ca\right)+\left(b-c\right)\left(bc-ca\right)\)
\(=\left(a-b\right)a\left(b-c\right)+\left(b-c\right)c\left(b-a\right)\)
\(=\left(a-b\right)a\left(b-c\right)-\left(b-c\right)c\left(a-b\right)\)
\(=\left(a-b\right)\left(b-c\right)\left(a-c\right)\)
mình làm vội, có chỗ nào sai bạn thông cảm nha
1.phân tích đa thức thành nhân tử
x3 - 5x2 + 8x - 4
= x3 - x2 - 4x2 + 4x + 4x - 4
= x2( x - 1 ) - 4x( x - 1 ) + 4( x - 1 )
= ( x - 1 )( x2 - 4x + 4 ) = ( x - 1 )( x - 2 )2
2.Cho các số a,b,c thỏa mãn a+b+c=3/2. Tìm giá trị nhỏ nhất của biểu thức P= a2 + b2 + c2
Áp dụng bất đẳng thức Cauchy-Schwarz dạng Engel ta có :
\(P=a^2+b^2+c^2=\frac{a^2}{1}+\frac{b^2}{1}+\frac{c^2}{1}\ge\frac{\left(a+b+c\right)^2}{1+1+1}=\frac{\left(\frac{3}{2}\right)^2}{3}=\frac{3}{4}\)
Đẳng thức xảy ra <=> a=b=c1/2. Vậy MinP = 3/4
\(x^8+x^7+1\)
\(=x^8+x^7+x^6-x^6+x^5-x^5+x^4-x^4+x^3-x^3+x^2-x^2+x-xx+1\)
\(=\left(x^8-x^6+x^5-x^3+x^2\right)\)
\(+\left(x^7-x^5+x^4-x^2+x\right)\)
\(+\left(x^6-x^4+x^3-x+1\right)\)
\(=\left(x^2+x+1\right)\left(x^6-x^4+x^3-x+1\right)\)
\(x^2-y^2+4x+4\)
\(=\left(x+2\right)^2-y^2\)
\(=\left(x+2+y\right)\left(x+2-y\right)\)
\(4x^2-y^2+8\left(y-2\right)\)
\(=4x^2-\left(y^2-8y+16\right)\)
\(=4x^2-\left(y-4\right)^2\)
\(=\left(2x+y-4\right)\left(2x-y+4\right)\)
\(a^4\left(b^2-c^2\right)+b^4\left(c^2-a^2\right)+c^4\left(a^2-b^2\right)\)
\(=a^4\left(b^2-c^2\right)+b^4\left(c^2-b^2+b^2-a^2\right)+c^4\left(a^2-b^2\right)\)
\(=a^4\left(b^2-c^2\right)+b^4\left(c^2-b^2\right)+b^4\left(b^2-a^2\right)+c^4\left(a^2-b^2\right)\)
\(=a^4\left(b^2-c^2\right)-b^4\left(b^2-c^2\right)-b^4\left(a^2-b^2\right)+c^4\left(a^2-b^2\right)\)
\(=\left(a^4-b^4\right)\left(b^2-c^2\right)+\left(c^4-b^4\right)\left(a^2-b^2\right)\)
\(=\left(a^2-b^2\right)\left(a^2+b^2\right)\left(b^2-c^2\right)-\left(b^2-c^2\right)\left(c^2+b^2\right)\left(a^2-b^2\right)\)
\(=\left(a^2-b^2\right)\left(b^2-c^2\right)\left(a^2+b^2-c^2-b^2\right)\)
\(=\left(a^2-b^2\right)\left(b^2-c^2\right)\left(a^2-c^2\right)\)
\(=\left(a-b\right)\left(a+b\right)\left(b-c\right)\left(b+c\right)\left(a-c\right)\left(a+c\right)\)
ap dung :(a-b-c)^2=a^2+b^2+c^2-2ab-2bc-2ca
ta dc:A=(a^2)^2+(b^2)^2+(c^2)^2-2.a^2.b^2-2.b^2-c^2-2.c^2.a^a
=>a=(a^2-b^2-c^2)^2