a: \(P\left(-1\right)=3-1+\dfrac{7}{4}=\dfrac{7}{4}+2=\dfrac{15}{4}\)

\(Q\left(\dfrac{1}{2}\right)=-3\cdot\dfrac{1}{4}+2\cdot\dfrac{1}{2}+2=-\dfrac{3}{4}+3=\dfrac{9}{4}\)

b: Đặt P(x)-Q(x)=0

\(\Leftrightarrow3x^2+x+\dfrac{7}{4}=-3x^2+2x+2\)

\(\Leftrightarrow6x^2-x-\dfrac{1}{4}=0\)

\(\Leftrightarrow24x^2-4x-1=0\)

\(\text{Δ}=\left(-4\right)^2-4\cdot24\cdot\left(-1\right)=112>0\)

Do đó: Phương trình có hai nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x_1=\dfrac{4-4\sqrt{7}}{48}=\dfrac{1-\sqrt{7}}{12}\\x_2=\dfrac{1+\sqrt{7}}{12}\end{matrix}\right.\)

g(x)=0<=>\(\left(\dfrac{2}{3}x+3\right)\left(\dfrac{3}{5}-1\right)=0\)<=>\(\left\{{}\begin{matrix}\dfrac{2}{3}x+3=0\\\dfrac{3}{5}x-1=0\end{matrix}\right.\)<=>\(\left\{{}\begin{matrix}x=\dfrac{-9}{2}\\x=\dfrac{5}{3}\end{matrix}\right.\)

Vậy .....

Nhiều nick nhỉ! :)

ai giúp cho 10 like

a)\(x\left(\dfrac{x^2}{2}-\dfrac{1}{2}x^3+\dfrac{1}{2}x\right)-\left(-\dfrac{1}{2}x^4+x^2\right)\)

\(\Leftrightarrow\dfrac{x^3}{2}-\dfrac{1}{2}x^4+\dfrac{1}{2}x^2-\dfrac{1}{2}x^4-x^2\)

\(\Leftrightarrow\dfrac{1}{2}x^2\left(x-x^2+1\right)-x^2\)

vậy bậc của đa thức là 2

b)\(Q\left(-\dfrac{1}{2}\right)=\dfrac{1}{2}\left(-\dfrac{1}{2}\right)^2\left[-\dfrac{1}{2}-\left(-\dfrac{1}{2}\right)^2+1\right]-\left(-\dfrac{1}{2}\right)^2\)

\(=\dfrac{1}{2}.\dfrac{1}{4}\left(-\dfrac{1}{2}-\dfrac{1}{4}+1\right)-\dfrac{1}{4}=\dfrac{1}{8}.\dfrac{1}{4}-\dfrac{1}{4}\)

\(=\dfrac{1}{32}-\dfrac{1}{4}=-\dfrac{7}{32}\)

a: Đặt A=0

=>-2/3x=5/9

hay x=-5/6

b: Đặt B(x)=0

=>(x-2/5)(x+2/5)=0

=>x=2/5 hoặc x=-2/5

c: Đặt C(X)=0

\(\Leftrightarrow x^3\cdot\dfrac{1}{2}=-\dfrac{4}{27}\)

\(\Leftrightarrow x^3=-\dfrac{8}{27}\)

hay x=-2/3

1) \(\dfrac{A\left(x-5\right)}{\left(x+1\right)\left(x-5\right)}=\dfrac{3x\left(x+3\right)}{\left(x+1\right)\left(x+3\right)}\)

\(\Rightarrow A=3x\)

2) \(\dfrac{\left(x+3\right)\left(x-2\right)}{A\left(x-3\right)}=\dfrac{\left(5x-1\right)\left(x-2\right)}{\left(5x-1\right)\left(x^2+3\right)}\)

\(\Leftrightarrow\dfrac{\left(x+3\right)}{A\left(x-3\right)}=\dfrac{1}{\left(x^2+3\right)}\)

\(\Rightarrow A=\dfrac{\left(x^2+3\right)\left(x+3\right)}{x-3}\)

3) \(\dfrac{\left(x-5\right)\left(x+5\right)}{\left(x+5\right)\left(2x-3\right)}=\dfrac{\left(x-5\right)A}{\left(2x-3\right)\left(x+2\right)}\)

\(\Leftrightarrow1=\dfrac{A}{\left(x+2\right)}\)

\(\Leftrightarrow A=x+2\)

a/  => \(\dfrac{3}{5}.\dfrac{1}{x}=\dfrac{6}{25}\)

=> \(\dfrac{1}{x}=\dfrac{2}{5}\)

=> x = 5/2

b/ \(\Rightarrow2\left(x-\dfrac{1}{3}\right)=\dfrac{2}{15}\)

=> \(x-\dfrac{1}{3}=\dfrac{1}{15}\)

=> \(x=\dfrac{2}{5}\)

c/ => | x + 1| = 10/21

=> \(\left[{}\begin{matrix}x=-\dfrac{11}{21}\\x=-\dfrac{31}{21}\end{matrix}\right.\)

d/ => \(5x+5=6x-3\)

=> x = 8

9.

hđt số 2 => x=30

Câu 2:

\(A=3\left(2x+9\right)^2-1>=-1\)

Dấu '=' xảy ra khi x=-9/2

Câu 9:

=>(x-30)^2=0

=>x-30=0

=>x=30

Câu 10:

\(=2x^2+6x-4x-12-2x^2-2x=-12\)

a: (2x-3/2)(|x|-5)=0

=>2x-3/2=0 hoặc |x|-5=0

=>x=3/4 hoặc |x|=5

=>\(x\in\left\{\dfrac{3}{4};5;-5\right\}\)

b: x-8x^4=0

=>x(1-8x^3)=0

=>x=0 hoặc 1-8x^3=0

=>x=1/2 hoặc x=0

c: x^2-(4x+x^2)-5=0

=>x^2-4x-x^2-5=0

=>-4x-5=0

=>x=-5/4

help me pls!!!