(X2+12X+36)(5-3X)≤0
Giải các phương trình sau:
a) 2 x − 10 4 − 5 = 2 x − 3 6 ;
b) x − 9 2 + x 2 − 81 = 0 ;
c) 3 x − 5 − 1 2 x + 9 = 0 ;
d) 1 2 x − 3 − 5 x = 3 2 x 2 − 3 x .
bài 1 giải các bất phương trình sau
a, -x2 +5x-6 ≥ 0
b, x2-12x +36≤0
c, -2x2 +4x-2≤0
d, x2 -2|x-3| +3x ≥ 0
e, x-|x+3| -10 ≤0
bài 2 xét dấu các biểu thức sau
a,<-x2+x-1> <6x2 -5x+1>
b, x2-x-2/ -x2+3x+4
c, x2-5x +2
d, x-< x2-x+6 /-x2 +3x+4 >
Bài 1:
a: \(\Leftrightarrow x^2-5x+6< =0\)
=>(x-2)(x-3)<=0
=>2<=x<=3
b: \(\Leftrightarrow\left(x-6\right)^2< =0\)
=>x=6
c: \(\Leftrightarrow x^2-2x+1>=0\)
\(\Leftrightarrow\left(x-1\right)^2>=0\)
hay \(x\in R\)
Tìm x biết:
1,
a,3x(x+1) - 2x(x+2) = -x-1
b,2x(x-2020) - x+2020 = 0
c,(x-4)2 - 36 = 0
d,x2 + 8x - 16 = 0
e,x(x+6) - 7x - 42 = 0
f,25x2 - 16 = 0
2,
a,3x3 - 12x = 0
b,x2 + 3x - 10 = 0
Bài 1:
a) \(\Rightarrow3x^2+3x-2x^2-4x+x+1=0\)
\(\Rightarrow x^2=-1\left(VLý\right)\Rightarrow S=\varnothing\)
b) \(\Rightarrow\left(x-2020\right)\left(2x-1\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=2020\\x=\dfrac{1}{2}\end{matrix}\right.\)
c) \(\Rightarrow\left(x-10\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=10\\x=-2\end{matrix}\right.\)
d) \(\Rightarrow\left(x+4\right)^2=0\Rightarrow x=-4\)
e) \(\Rightarrow\left(x+6\right)\left(x-7\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=-6\\x=7\end{matrix}\right.\)
f) \(\Rightarrow\left(5x-4\right)\left(5x+4\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=\dfrac{4}{5}\\x=-\dfrac{4}{5}\end{matrix}\right.\)
Bài 2:
a) \(\Rightarrow3x\left(x^2-4\right)=0\Rightarrow3x\left(x-2\right)\left(x+2\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2\end{matrix}\right.\)
b) \(\Rightarrow x\left(x-2\right)+5\left(x-2\right)=0\Rightarrow\left(x-2\right)\left(x+5\right)=0\)
\(\Rightarrow\left[{}\begin{matrix}x=2\\x=-5\end{matrix}\right.\)
Giải các phương trình:
a) x + 1 3 x − 2 = 0 ; b) x 2 + 1 2 x − 5 = 0 ;
c) x 2 2 x − 3 − 9 2 x − 3 = 0 ; d) 2 x 2 − 3 x + 1 = 0 .
a, x2 - 4x = 0 b, (2x + 1)2 - 4x (x + 3) = 9
c, x2 -12x = -36
\(x\left(x-4\right)=0\Leftrightarrow\left[{}\begin{matrix}x=0\\x-4=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=4\end{matrix}\right.\)
\(4x^2+4x+1-4x^2-12x-9=0\)
\(-8x-8=0\Leftrightarrow x=-1\)
\(\left(x-6\right)^2=0\)
\(x-6=0\Leftrightarrow x=6\)
c)\(x^2-12x=-36\)
\(x^2-12x+36=0\)
\(\left(x-6\right)^2=0\)
\(\Rightarrow x-6=0\)
........
1. Rút gọn
a, A=(4x+3y)2 + (4x-3y)2
b,B=(x-23)-(x+2)3
c,C=(x+2y)2+2.(x+2y) (x-2y) + (x-2y)2
2. Tìm x
a, x2+12x+36=0
b,16x2-8x+1=0
c,x3+3x2+3x+1=0
2a) pt <=> (x + 6)^2 = 0
<=> x = -6
b) pt <=> (4x - 1)^2 = 0
<=> x = 1/4
c) pt<=> (x + 1)^3 = 0
<=> x = -1
Bài 1:
a: Ta có: \(A=\left(4x+3y\right)^2+\left(4x-3y\right)^2\)
\(=16x^2+24xy+9y^2+16x^2-24xy+9y^2\)
\(=32x^2+18y^2\)
b: Ta có: \(B=\left(x-2\right)^3-\left(x+2\right)^3\)
\(=x^3-6x^2+12x-8-x^3-6x^2-12x-8\)
\(=-12x^2-24\)
1. Rút gọn
a, A=(4x+3y)2 + (4x-3y)2
b,B=(x-23)-(x+2)3
c,C=(x+2y)2+2.(x+2y) (x-2y) + (x-2y)2
2. Tìm x
a, x2+12x+36=0
b,16x2-8x+1=0
c,x3+3x2+3x+1=0
Bài 2:
a: Ta có: \(x^2+12x+36=0\)
\(\Leftrightarrow x+6=0\)
hay x=-6
b: Ta có: \(16x^2-8x+1=0\)
\(\Leftrightarrow4x-1=0\)
hay \(x=\dfrac{1}{4}\)
Bài 1:
a: Ta có: \(A=\left(4x+3y\right)^2+\left(4x-3y\right)^2\)
\(=16x^2+24xy+9y^2+16x^2-24xy+9y^2\)
\(=32x^2+18y^2\)
b: Ta có: \(B=\left(x-2\right)^3-\left(x+2\right)^3\)
\(=x^3-6x^2+12x-8-x^3-6x^2-12x-8\)
\(=-12x^2-24\)
c: Ta có: \(C=\left(x+2y\right)^2+2\left(x+2y\right)\left(x-2y\right)+\left(x-2y\right)^2\)
\(=\left(x+2y+x-2y\right)^2\)
\(=4x^2\)
3x^2-4xy+2y^2-12x+36=0
Bài này tìm x,y à bạn?:\(3x^2-4xy+2y^2-12x+36=0\)
\(< =>2x^2-4xy+2y^2+x^2-12x+36\)
\(< =>x^2-2xy+y^2+x^2-2xy+y^2+x^2-12x+36=0\)
\(< =>\left(x-y\right)^2+\left(x-y\right)^2+\left(x-6\right)^2=0\)
\(< =>2\left(x-y\right)^2+\left(x-6\right)^2=0\)
\(=>\left[{}\begin{matrix}2\left(x-y\right)^2=0\\\left(x-6\right)^2=0\end{matrix}\right.\)\(=>x=y=6\)
giải pt :
a, \(729x^4+8\sqrt{1-x^2}=36\)
b, \(3x^2-12x-5\sqrt{10+4x-x^2}+12=0\)
a.
ĐKXĐ: \(-1\le x\le1\)
Đặt \(\sqrt{1-x^2}=t\Rightarrow0\le t\le1\)
\(x^2=1-t^2\Rightarrow x^4=t^4-2t^2+1\)
Pt trở thành:
\(729\left(t^4-2t^2+1\right)+8t=36\)
\(\Leftrightarrow729t^4-1458t^2+8t+693=0\)
\(\Leftrightarrow\left(9t^2+2t-9\right)\left(81t^2-18t-77\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}9t^2+2t-9=0\\81t^2-18t-77=0\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}t=\dfrac{\sqrt{82}-1}{9}\\t=\dfrac{1+\sqrt{78}}{9}\end{matrix}\right.\)
\(\Rightarrow x=\pm\sqrt{1-t^2}=...\)
b.
ĐKXĐ: ...
\(-3\left(10+4x-x^2\right)-5\sqrt{10+4x-x^2}+42=0\)
Đặt \(\sqrt{10+4x-x^2}=t\ge0\)
\(\Rightarrow-3t^2-5t+42=0\)
\(\Rightarrow\left[{}\begin{matrix}t=3\\t=-\dfrac{14}{3}\left(loại\right)\end{matrix}\right.\)
\(\Rightarrow\sqrt{10+4x-x^2}=3\)
\(\Leftrightarrow x^2-4x-1=0\)
\(\Leftrightarrow x=...\)