\(\left(5x-1\right)^2-\left(5x-4\right)\left(5x+4\right)=7\)

\(25x^2-10x+1-25x^2+16=7\)

\(17-10x=7\)

\(10x=10\)

\(x=1\)

a, \(-4x+5+2x-1=3\Leftrightarrow-2x=-1\Leftrightarrow x=\dfrac{1}{2}\)

b, \(-2x+2=2\Leftrightarrow x=0\)

c, \(-2x-6=-8\Leftrightarrow x=1\)

ta có 

a. (5x-7)(x-9)-(-x+3)(-5x+2)= 2x(x-4)-(x-1)(2x+3)

\(\Leftrightarrow5x^2-52x+63-\left(5x^2-17x+6\right)=2x^2-8x-\left(2x^2+x-3\right)\)

\(\Leftrightarrow-35x+57=-9x+3\Leftrightarrow26x=54\Leftrightarrow x=\frac{27}{13}\)

b. (x-3)(-x+10)+(x-8)(x+3)= (5x^2-1)(x+3)-5x^3-15x^2

\(\Leftrightarrow-x^2+13x-30+x^2-5x-24=5x^3+15x^2-x-3-5x^3-15x^2\)

\(\Leftrightarrow8x-54=-x-3\Leftrightarrow9x=51\Leftrightarrow x=\frac{17}{3}\)

bai dai dong qua

a) (x-2)^3-x(x+1)(x-1)+6x(x-3)=0

\(x^3-6x^2+12x-8-x\left(x^2-1\right)+6x\left(x-3\right)=0\)

\(x^3-6x^2+12x-8-x^3+x+6x^2-18x=0\)

\(-5x-8=0\)

\(x=-\frac{8}{5}\)

Mai mik làm mấy bài kia sau

2/

b) ( cái bài này chịu)

c) (x+1)^3-(x-1)^3-6(x-1)^2=-10

(x+1-x+1)\(\left[\left(x+1\right)^2+\left(x+1\right)\left(x-1\right)+\left(x-1\right)^2\right]\)\(-6\left(x^2-2x+1\right)=-10\)

\(2\left(x^2+2x+1+x^2-1+x^2-2x+1\right)-6x^2+12x-6=-10\)

\(2\left(3x^2+1\right)-6x^2+12x-6=0\)

\(6x^2+2-6x^2+12x-6=-10\)

\(12x=-10+4\)

\(12x=-6=>x=-\frac{1}{2}\)

d) (5x-1)^2-(5x-4)(5x+4)=7

\(25x^2-10x+1-25x^2+16=7\)

-10x = 7 - 17

-10x = -10

x= 1

Câu còn lại bn làm tương tự

3/

a) 

Ta có: 

(a+b+c)^2=3(ab+bc+ca)

a^2 + b^2 + c^2 + 2ab + 2ac + 2bc = 3ab + 3bc + 3ac

a^2 + b^2 + c^2 + 2ab + 2ac + 2bc - 3ab - 3bc - 3ac = 0

a^2 + b^2 + c^2  - ac - bc - ab = 0

2a^2 + 2b^2 + 2c^2  - 2ac - 2bc - 2ab = 0

(a²-2ab+b²⁾+(a²-2ac+c²) + (b²-2bc +c²) = 0

(a-b)^2 + (a-c)^2 + (b-c)^2 =0

=> a=b=c

a) (5x+1)²-(5x+3).(5x-3)=30

\(\Leftrightarrow25x^2+10x+1-25x^2+9-30=0\)

\(\Leftrightarrow10x-20=0\)

\(\Leftrightarrow10x=20\)

\(\Leftrightarrow x=2\)

b) (x-3).(x²+3x+9)+x.(x+2).(2-x)=1

\(\Leftrightarrow x^3-3^3+x\left(4-x^2\right)-1=0\)

\(\Leftrightarrow x^3-27+4x-x^3-1=0\)

\(\Leftrightarrow4x-28=0\)

\(\Leftrightarrow4x=28\)

\(\Leftrightarrow x=7\)

câu a cái ngoặc của 5x+1

a)\(\left(5x-1\right)^2-\left(5x-4\right)\left(5x+4\right)=7\)

\(\Leftrightarrow25x^2-10x+1-25x^2+16=7\)

\(\Leftrightarrow-10x=-10\)

\(\Leftrightarrow x=1\)

b) k hiểu đề

1. a) \(( 5x-1)^2 - (5x-4) ( 5x+4) = 7\)

\(\Leftrightarrow\)\(25x^2-10x+1-(25x^2-16)=7\)

\(\Leftrightarrow\)\(25x^2-10x+1-25x^2+16-7=0\)

\(\Leftrightarrow\)\(10x=10\)

\(\Rightarrow x=1\)

b) \(( 4x-1)^2 - (2x+3)^2 + 5(x+2)^2 + 3(x-2) ( x+2) = 500\)

\(\Leftrightarrow\)\(16x^2-8x+1-4x^2-12x-9+5x+10+3x^2-12=500\)

\(\Leftrightarrow\)\(15x^2-15x=510\)

\(\Leftrightarrow\)\(15(x^2-x)=510\)

\(\Leftrightarrow\)\(x^2-x=34\)

\(\Rightarrow x=-5,352349955\)

c) \((x-2)^3 - (x-2) ( x^2+2x+4 ) + 6(x-2)(x+2) = 60\)

\(\Leftrightarrow x^3-6x^2+12x-8-\left(x^3-2^3\right)+6\left(x^2-4\right)=60\)

\(\Leftrightarrow x^3-6x^2+12x-8-x^3+8+6x^2-24=60\)

\(\Leftrightarrow12x-24=60\)

\(\Leftrightarrow12x=84\)

\(\Rightarrow x=7\)

b. 6x(x - 5) - x(6x + 3)

= x(6x - 30) - x(6x + 3)

= x(6x - 30 - 6x - 3)

= x(-33)

= -33x