\(4\times\left(x+5\right)^3-7=101\)

\(\Rightarrow4\times\left(x+5\right)^3=101+7\)

\(\Rightarrow4\times\left(x+5\right)^3=108\)

\(\Rightarrow\left(x+5\right)^3=108\div4\)

\(\Rightarrow\left(x+5\right)^3=27\)

\(\Rightarrow\left(x+5\right)^3=3^3\)

\(\Rightarrow x+5=3\)

\(\Rightarrow x=3-5\)

\(\Rightarrow x=-2\)

Keuka

4(x+5)³-7=101

4(x+5)³=101+7

4(x+5)³=108

(x+5)³=108:4

(x+5)³=27

(x+5)³=3³

=> x+5=3

x=3-5

x=-2

Vậy x=-2

A = 3x - x²

C₁: A = \(\left(\sqrt{3x}\right)^2-x^2\)

A = \(\left(\sqrt{3x}-x\right)\left(\sqrt{3x}+x\right)\)

C₂: x(3 - x)

Mình ghi thiếu .Tìm giá trị ớn nhất

1)

\((x+2)(x+3)(x+4)(x+5)-24\\=[(x+2)(x+5)]\cdot[(x+3)(x+4)]-24\\=(x^2+7x+10)(x^2+7x+12)-24\)

Đặt \(x^2+7x+10=y\), khi đó biểu thức trở thành:

\(y(y+2)-24\\=y^2+2y-24\\=y^2+2y+1-25\\=(y+1)^2-5^2\\=(y+1-5)(y+1+5)\\=(y-4)(y+6)\\=(x^2+7x+10-4)(x^2+7x+10+6)\\=(x^2+7x+6)(x^2+7x+16)\)

2) Bạn xem lại đề!

x² - 4x + 2 = ( x² - 4x + 4 ) - 2 = ( x - 2 )² - 2 ≥ -2 ∀ x

Dấu "=" xảy ra <=> x = 2 . Vậy GTNN của bthuc = -2

x^2 - 4x + 2 

= x^2 - 4x + 4 - 2 

= ( x - 2 ) ^2 - 2 

 \(\left(x-2\right)^2\ge0\forall x\)

\(\left(x-2\right)^2-2\ge-2\)   

Dấu = xảy ra khi và chỉ khi 

 x - 2 = 0 

x = 0 + 2 

x = 2 

vậy min = -2 khi và chỉ khi x = 2 

đặt A = x² -4x +2

= ( x² -4x +4) -2

= ( x-2)² -2

ta có : ( x-2 )² \(\ge0\forall x\) => ( x-2 )² 

Dấu  = xảy ra <=> ( x-2)² =0

                         => x-2=0 => x=2

Vậy GTNN của A = -2 tại x=2

7x+2/5x+7=7x-1/5x+1=>37/5x+7=34/5x+1=>37/5x-34/5x=1-7=>3/5x=-6=>x=-6:3/5=-10 vay x=-10 nho ****

1, \(2x^2+4x=2x\left(x+2\right)\)

2, \(15x^3+5x^2-10x=5x\left(3x^2+x-2\right)=5x\left(x-\dfrac{2}{3}\right)\left(x+1\right)\)

3) \(5x^2\left(x-2y\right)+15x\left(x-2y\right)=\left(5x^2+15x\right)\left(x-2y\right)=5x\left(x+3\right)\left(x-2y\right)\)

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

5) \(5x^2-10x=5x\left(x-2\right)\)

6) \(3x-6y=3\left(x-2y\right)\)

7) \(25x^2+5x^3+x^2y=x^2\left(25+5x+y\right)\)

8) \(14x^2y-21xy^2+28x^2y^2=7xy\left(2x-3y+4xy\right)\)

9) \(x\left(y-1\right)-y\left(y-1\right)=\left(x-1\right)\left(y-1\right)\)

10) \(10x\left(x-y\right)-8y\left(y-x\right)=\left(10x+8y\right)\left(x-y\right)=2\left(5x+4y\right)\left(x-y\right)\)

\(1,=2x\left(x+2\right)\\ 2,=5x\left(3x^2+x-2\right)\\ 3,=\left(x-2y\right)\left(5x^2+15x\right)=5x\left(x+3\right)\left(x-2y\right)\\ 4,=\left(x-y\right)\left(3-5x\right)\\ 5,=5x\left(x-2\right)\\ 6,=3\left(x-2y\right)\\ 7,=5x^2\left(5+x+y\right)\\ 8,=7xy\left(2x-3y+4xy\right)\\ 9,=\left(y-1\right)\left(x-y\right)\\ 10,=\left(x-y\right)\left(10x+8y\right)=2\left(5x+4y\right)\left(x-y\right)\)

\(ĐK:x\ge-3\\ PT\Leftrightarrow\sqrt{x-3}=2\Leftrightarrow x-3=4\Leftrightarrow x=7\left(tm\right)\)

\(\left|x+1\right|+\left|x+4\right|=3x\)

\(\Rightarrow1+x+4+x=3x\)

\(\Rightarrow5+2x=3x\)

\(\Rightarrow5=3x-2x\)

\(\Rightarrow5=x\)