Đề sai nhé bạn . a=b=c=0 thì phân số 1/a không có nghĩa!

http://tailieu.tv/tai-lieu/phuong-phap-nhan-luong-lien-hop-giai-cac-bai-toan-ve-phuong-trinh-vo-ti-28140/

Vào link này mà xem

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a) \(a^2+b^2=a^2+\frac{1}{4}+b^2+\frac{1}{4}-\frac{1}{2}\)  

\(\ge2\sqrt{a^2.\frac{1}{4}}+2\sqrt{b^2.\frac{1}{4}}-\frac{1}{2}\) (bdt cosi)

\(=a+b-\frac{1}{2}=1-\frac{1}{2}=\frac{1}{2}\) (vi a+b=1)

dau = xay ra <=> a=b=1/2

chuc ban hoc tot

mik phai di ngu nen lam hoi tat mong bn thong cam

phan b bn lam tuong tu nha

1/ Ta có:

\(\left(a-b\right)^2\ge0,\) mọi a, b

<=> \(a^2-2ab+b^2\ge0\)

<=> \(2a^2+2b^2\ge a^2+2ab+b^2\)

<=> \(2\left(a^2+b^2\right)\ge\left(a+b\right)^2\)

<=> \(a^2+b^2\ge\frac{\left(a+b\right)^2}{2}=\frac{1}{2}\)

Dấu bằng xảy ra <=>  a - b = 0 <=> a  = b.

2/ Dựa vào câu 1. 

\(a^4+b^4\ge\frac{\left(a^2+b^2\right)^2}{2}\ge\frac{\left(\frac{1}{2}\right)^2}{2}=\frac{1}{8}\).

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

\(=x^2-2x+1-\left(x+2\right)\left[2x-4+3\left(x^2+4x+4\right)\right]\)

\(=x^2-2x+1-\left(x+2\right)\left(3x^2+14x+8\right)\)

\(=x^2-2x+1-\left(3x^3+6x^2+14x^2+28x+8x+16\right)\)

\(=-3x^3-21x^2-38x-15\)

b. x⁴ - x² - 2x - 1

=x⁴-(x²+2x+1)

=x⁴-(x+1)²

=(x²-x-1)(x²+x+1)

d. ( x² + 3x + 1 ) ( x² + 3x - 3 ) - 5

Đặt x²+3x=y

=> (y+1)(y-3)-5=y²-2y-8=(y-1)²-9

=(y-4)(y+2)

=(x²+3x-4)(x²+3x+2)=(x-1)(x+4)(x+1)(x+2)

\(E=\left(x^3+3xy^2+3x^2y+y^3\right)+3\left(x+y\right)-3\left(x^2+2xy+y^2\right)+2016\)

\(=\left(x+y\right)^3+3\left(x+y\right)-3\left(x+y\right)^2+2016\)

\(=21^3+3.21-3.21^2+2016\)

\(=\left(21-1\right)^3+2017=8000+2017=10017\)

Mình không viết lại đề nha ~

\(E=\left(x^3+3xy^2+3x^2y+y^3\right)+\left(3y+3x\right)+\left(3x^2+6xy+3y^2\right)+2016\)

\(E=\left(x+y\right)^3+3\left(x+y\right)+3\left(x+y\right)^2+2016\)

\(E=\left(x+y\right)[\left(x+y\right)^2+3+\left(x+y\right)]+2016\)

\(E=21\left(21^2+3+21\right)+2016\)

\(E=21.465+2016\)

\(E=9765+2016=11781\)