a: Đặt 3x-5=0

=>3x=5

hay x=5/3

b: Đặt 3-1/2x=0

=>1/2x=3

hay x=6

c: Đặt x²+3x+2=0

=>(x+2)(x+1)=0

=>x=-2 hoặc x=-1

d: Đặt 5x²+7x+2=0

=>(5x+1)(x+1)=0

=>x=-1 hoặc x=-1/5

Chọn: B

a) \(\frac{3}{4}+\frac{2}{5}x=\frac{29}{60}\)

\(\frac{2}{5}x=\frac{29}{60}-\frac{3}{4}\)

\(\frac{2}{5}x=\frac{-4}{15}\)

\(x=\frac{-4}{15}:\frac{2}{5}\)

\(x=\frac{-2}{3}\)

b) \(x^4=16\)

\(x^4=2^4\)

\(x=2\)

c) \(\left(x+5\right)^3=-64\)

\(\left(x+5\right)^3=-4^3\)

\(x+5=-4\)

\(x=-4-5\)

\(x=-9\)

d) \(\left(x-\frac{3}{4}\right)^2=0\)

\(\left(x-\frac{3}{4}\right)^2=0^2\)

\(x-\frac{3}{4}=0\)

\(x=0+\frac{3}{4}\)

\(x=\frac{3}{4}\)

e) \(x:8,5=0,69:\left(-1,15\right)\)

\(x:8,5=-0,6\)

\(x=-0,6.8,5\)

\(x=-5,1\)

A.2/5x=29/60-3/4

2/5x=29/60-45/60

2/5x=-4/15

x=-4/15:2/5

x=4/15.5/2 

x=-2/3

B. x mũ 4 = 42

-) x=2

C. (x+5) mũ 3 = -4 3

x+5 = -4

X= -4-5

X=-9

D. ( X -3/4)mũ 2=0 mũ 2

X= 0+3/4

X=3/4

E. X:8,5=-0,6

X=-0,6*8,5

X=5,1

Lời giải:

Ta có:

\(y'=(e^x+e^{-x})'=e^x-e^{-x}=e^x-\frac{1}{e^x}\)

\(y'=0\Leftrightarrow e^x-\frac{1}{e^x}=0\Leftrightarrow e^{2x}-1=0\)

\(\Leftrightarrow e^{2x}=1\Leftrightarrow 2x=0\Leftrightarrow x=0\)

a) \(\dfrac{x}{5}=\dfrac{2}{5}\)

\(\Rightarrow5x=10\)

\(\Leftrightarrow x=2\)

Vậy x = 2

b) ĐKXĐ: \(x\ne0\)

 \(\dfrac{3}{-8}=\dfrac{6}{-x}\)

\(\Rightarrow-3x=-48\)

\(\Leftrightarrow x=16\)

Vậy x = 16

c) \(\dfrac{1}{9}=\dfrac{-2x}{10}\)

\(\Rightarrow-18x=10\)

\(\Leftrightarrow x=-\dfrac{5}{9}\)

Vậy \(x=-\dfrac{5}{9}\)

d) ĐKXĐ: \(x\ne0\)

 \(\dfrac{3}{x}-5=\dfrac{-9}{x}+2\)

\(\Leftrightarrow\dfrac{3-5x}{x}=\dfrac{-9+2x}{x}\)

\(\Rightarrow3-5x=-9+2x\)

\(\Leftrightarrow7x=12\)

\(\Leftrightarrow x=\dfrac{12}{7}\)

Vậy \(x=\dfrac{12}{7}\)

e) ĐKXĐ: \(x\ne0\)

 \(\dfrac{x}{-2}=\dfrac{-8}{x}\)

\(\Rightarrow x^2=16\)

\(\Leftrightarrow x=\pm4\)

Vậy \(x=\pm4\)

a) Ta có: \(\dfrac{x}{5}=\dfrac{2}{5}\)

\(\Leftrightarrow x=\dfrac{2\cdot5}{5}=2\)

Vậy: x=2

b) Ta có: \(\dfrac{3}{-8}=\dfrac{6}{-x}\)

\(\Leftrightarrow-x=\dfrac{6\cdot\left(-8\right)}{3}=-16\)

hay x=16

Vậy: x=16

a.\(3x^2-11x+6\)

= \(3x^2-9x-2x+6\)

=\(3x\left(x-3\right)-2\left(x-3\right)\)

=\(\left(x-3\right)\left(3x-2\right)\)

b\(8x^2+10x-3\)

=.\(8x^2-2x+12x-3\)

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

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

d.\(x^2-y^2+10x-6y+16\)

=\(\left(x^2+10x+25\right)-\left(y^2+6y+9\right)\)

=\(\left(x+5\right)^2-\left(y+3\right)^2\)

=\(\left(x+5-y-3\right)\left(x+5+y+3\right)\)

=\(\left(x-y+2\right)\left(x+y+8\right)\)

e.\(x^4+x^2y^2+y^4\)

=\(x^4+2x^2y^2+y^4-x^2+y^2\)

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

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

a)

\(=3x^2-9x-2x+6=3x\left(x-3\right)-2\left(x-3\right)=\left(x-3\right)\left(3x-2\right)\)

b)

\(=8x^2-2x+12x-3=2x\left(4x-1\right)+3\left(4x-1\right)=\left(4x-1\right)\left(2x+3\right)\)

A) \(x^2+y^2=\left(x+y\right)^2-2xy=\left(-3\right)^2-2.\left(-10\right)=9+20=29\)

B) \(x^3+y^3=\left(x+y\right)^3-3xy\left(x+y\right)=\left(-3\right)^3-3\left(-10\right)\left(-3\right)=-27-90=-117\)

a) x=1/6

b) x=0 và x =1

c) x=-2 và x = 2

d) x = 1

e) x = 5 và x = -1

g) x = 1 và x = 4

h) Đa thức không có nghiệm.