( x-5 )2-x ( x+3 )=6 x
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
= (a+1)(a-1)(a+2)(a-2)
= \(\left(a^2-1\right)\left(a^2-4\right)=a^4-4a^2-a^2+4=a^4-5a^2+4\)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có \(\left(a+b+c\right)^2=0\Leftrightarrow a^2+b^2+c^2+2ab+2bc+2ac=0\)
\(\Leftrightarrow1+2\left(ab+bc+ac\right)=0\Leftrightarrow ab+bc+ac=-\dfrac{1}{2}\)
\(\Leftrightarrow\left(ab+bc+ac\right)^2=\dfrac{1}{4}\Leftrightarrow a^2b^2+b^2c^2+c^2a^2+2abc\left(a+b+c\right)=\dfrac{1}{4}\)
\(\Leftrightarrow a^2b^2+b^2c^2+c^2a^2=\dfrac{1}{4}\)
-> \(\left(a^2+b^2+c^2\right)^2=a^4+b^4+c^4+2a^2b^2+2b^2c^2+2c^2a^2=1\)
\(\Leftrightarrow a^4+b^4+c^4=1-\dfrac{2.1}{4}=\dfrac{1}{2}\)
\(a+b+c=0\)
\(\left(a+b+c\right)^2=0\)
\(a^2+b^2+c^2+2\left(ab+bc+ca\right)=0\)
\(2\left(ab+bc+ca\right)=-1\left(a^2+b^2+c^2=1\right)\)
\(ab+bc+ca=-\dfrac{1}{2}\)
\(\left(ab+bc+ca\right)=\dfrac{1}{4}\)
\(\left(ab\right)^2+\left(bc\right)^2+\left(ca\right)^2+2abc\left(a+b+c\right)=\dfrac{1}{4}\)
\(\left(ab\right)^2+\left(bc\right)^2+\left(ca\right)^2=\dfrac{1}{4}\left(a+b+c=0\right)\)
+) \(a^2+b^2+c^2=1\)
\(\left(a^2+b^2+c^2\right)^2=1\)
\(a^4+b^4+c^4+2\left(a^2b^2+b^2c^2+c^2a^2\right)=1\)
\(a^4+b^4+c^4=1-\dfrac{1}{2}=\dfrac{1}{2}\left(a^2b^2+b^2c^2+c^2a^2=\dfrac{1}{4}\right)\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{x}{18}\) = \(\dfrac{y}{15}\) = \(\dfrac{x-y}{18-15}\) = \(\dfrac{-6}{3}\) = -2
x = 18. (-2) = -36
y = 15 x (-2) = -30
x/18 = y/15 và x-y = -6
=> x/18 = y/15 => x-y/ 18-15 => -6 / 3 = -2
=> x = -2 . 18 = -36
=> y = -2 . 15 = -30
![](https://rs.olm.vn/images/avt/0.png?1311)
a) A\(=x^2+y^2+2x+15-6y\)
\(=x^2+y^2+2x+9+5+1-6y\)
\(=\left(x^2+2x+1\right)+\left(y^2-6y+9\right)+5\)
\(=\left(x+1\right)^2+\left(y-3\right)^2+5\)
Vì \(\left(x+1\right)^2\) luôn dương với mọi x
\(\left(y-3\right)^2\) luôn dương với mọi y
\(\Rightarrow\left(x+1\right)^2+\left(y-3\right)^2+5\) \(\ge5>0\)
Vậy biểu thức A luôn dương với mọi x, y
Câu b) bạn làm tương tự nha
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
( x-5 )2-x ( x+3 )=6 x
<=> (x-5) - x2 -3x =6x
<=> x2 + 8x + 5= 0
<=> x= -4+ \(\sqrt{11}\);-4- \(\sqrt{11}\)