Dạ e cảm ơn nhiều ạ

`@` `\text {Ans}`

`\downarrow`

`3^3 * x^2 - 2^4 * x^2 = 8^2 * 5 - 4^2 * 3^2`

`=> x^2 . (3^3 - 2^4) = 2^6 . 5 - 2^4 . 3^2`

`=> x^2 . 11 = 2^4 . (2^2 . 5 - 3^2)`

`=> x^2 . 11 = 2^4 . 11`

`=> x^2 . 11 - 2^4 . 11 = 0`

`=> 11 . (x^2 - 16) = 0`

`=> x^2 - 16 = 0`

`=> x^2 = 16`

`=> x^2 = (+-4)^2`

`=> x = `\(\pm4\)

Vậy, `x \in`\(\left\{4;-4\right\}\)

_____

\(\left[\left(\dfrac{1}{2}\right)^2-\left(\dfrac{1}{3}\right)^3\right]x+3^2\cdot2^2=4^2\cdot3\)

`=>`\(\left(\dfrac{1}{4}-\dfrac{1}{27}\right)x+\left(3\cdot2\right)^2=48\)

`=>`\(\dfrac{23}{108}\cdot x+6^2=48\)

`=>`\(\dfrac{23}{108}x=48-6^2\)

`=>`\(\dfrac{23}{108}x=48-36\)

`=>`\(\dfrac{23}{108}x=12\)

`=>`\(x=\dfrac{1296}{23}\)

Vậy, `x = `\(\dfrac{1296}{23}\)

\(3^3.x^2-2^4.x^2=8^2.5-4^3.3^2\)

\(\Leftrightarrow x^2\left(27-16\right)=2^6.5-2^6.9\)

\(\Leftrightarrow11x^2=2^6.\left(5-9\right)=-4.2^6=-2^8\)

\(\Leftrightarrow x^2=-\dfrac{2^6}{11}< 0\)

\(\Rightarrow x\in\varnothing\)

\(\left[\left(\dfrac{1}{2}\right)^2-\left(\dfrac{1}{3}\right)^3\right]x+3^2.2^2=4^2.3\)

\(\Leftrightarrow\left(\dfrac{1}{4}-\dfrac{1}{27}\right)x+36=48\)

\(\Leftrightarrow\dfrac{23}{108}x=12\Leftrightarrow x=\dfrac{12.108}{23}=\dfrac{1296}{23}\)

\(\Leftrightarrow x^2-6x+9-4x^2-4x-1-2\left(x^2+x-2\right)=3\left(x-3\right)-\left(4x^2+8x-x-2\right)\)

\(\Leftrightarrow-3x^2-10x+8-2x^2-2x+4=3\left(x-3\right)-4x^2-7x+2\)

\(\Leftrightarrow-5x^2-12x+12=3x-9-4x^2-7x+2\)

\(\Leftrightarrow-5x^2-12x+12=-4x^2-4x-7\)

\(\Leftrightarrow-4x^2-4x-7+5x^2+12x-12=0\)

\(\Leftrightarrow x^2+8x-19=0\)

\(\text{Δ}=8^2-4\cdot1\cdot\left(-19\right)=76+64=140\)

Vì Δ>0 nên phương trình có hai nghiệm phân biệt là:

\(\left\{{}\begin{matrix}x_1=\dfrac{-8-2\sqrt{35}}{2}=-4-\sqrt{35}\\x_2=-4+\sqrt{35}\end{matrix}\right.\)

\(\left(4x+1\right)\left(x-3\right)-\left(x-7\right)\left(4x-1\right)=15\)

\(4x^2-11x-3-\left(4x^2-29x+7\right)=15\)

\(4x^2-11x-3-4x^2+29x-7=15\)

\(18x-10=15\)

\(x=\frac{25}{18}\)

Ta có:

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

\(\Rightarrow16x^2-16x-5-4\left(x^2-1\right)=7\)

\(\Rightarrow16x^2-16x-5-4x^2+4=7\)

\(\Rightarrow12x^2-16x=8\)

\(\Rightarrow3x^2-4x=2\)

\(\Rightarrow3\left(x^2-2.\frac{2}{3}.x+\left(\frac{2}{3}\right)^2\right)=2\)

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

\(\Rightarrow\orbr{\begin{cases}x-\frac{2}{3}=\sqrt{\frac{2}{3}}\\x-\frac{2}{3}=-\sqrt{\frac{2}{3}}\end{cases}}\)\(\Rightarrow\orbr{\begin{cases}x=\sqrt{\frac{2}{3}}+\frac{2}{3}\\x=\frac{2}{3}-\sqrt{\frac{2}{3}}\end{cases}}\)

|5x-3| - 3x = 7

*Nếu \(x\ge\frac{3}{5}\)

5x - 3 - 3x = 7

2x = 10

x = 5 ( tm)

*Nếu \(x< \frac{3}{5}\)

3 - 5x - 3x = 7

-8x = 4 

x = \(-\frac{1}{2}\)( tm )

Làm hơi khó nhìn , thông cảm. Mệt rùi :)

|x - 3| + |x - 5| - 4x = -28

*Nếu x < 3

3 - x + 5 - x - 4x = -28

-6x = -36

x = 6 ( loại do ko tm khoảng đang xét )

* nếu 3 < x < 5

x - 3 + 5 - x - 4x = -28

-4x = -30

x= \(\frac{15}{2}\) ( loại do ko tm khaongr đang xét )

*Nếu x > 5

x - 3 + x - 5 - 4x = -28

-2x = -20

x = 10 ( tm)

Vậy x =10

Lời giải:
a)

\((4x-1)^2+(3x+1)^2+2(4x-1)(3x+1)\)

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

\(=[(4x-1)+(3x+1)]^2=(7x)^2=49x^2\)

b)

\((x^2+2)(x-5)+(x-5)(x^2+5x+25)\)

\(=(x-5)[(x^2+2)+(x^2+5x+25)]\)

\(=(x-5)(2x^2+5x+27)\)