Question

[Trần Đức Mạnh]

Bài 1: Tìm x

a) \(\left(5-2x\right)^2-16=0\)

b) \(x^2-4x=29\)

c) \(\left(x-3\right)^3-\left(x-3\right).\left(x^2+3x+9\right)+9.\left(x+1\right)^2=15\)

d) \(2.\left(x-5\right).\left(x+5\right)-\left(x+2\right).\left(2x-3\right)+x.\left(x^2-8\right)=\left(x+1\right).\left(x^2-x+1\right)\)

Bài 2: Rút gọn

a) \(\left(x^2+x+1\right).\left(x^2-x+1\right).\left(x^2-1\right)\)

b) \(\left(a+b-c\right)^2+\left(a-b+c\right)^2-2.\left(b-c\right)^2\)

c) \(\left(a+b+c\right)^2-\left(a+b\right)^2-\left(a+c\right)^2-\left(b+c\right)^2\)

d) \(\left(a+b+c\right)^2+\left(a-b-c\right)^2+\left(b-c-a\right)^2+\left(c-a-b\right)^2\)

Answer 1

[Tài Nguyễn Tuấn]

1. a) $(5-2x)^2-16=0$

$=>(5-2x)^2-4^2=0$

$=>(5-2x-4)(5-2x+4)=0$

$=>(1-2x)(9-2x)=0$

\(=>\left[{}\begin{matrix}1-2x=0=>x=0,5\\9-2x=0=>x=4,5\end{matrix}\right.\)

b) $x^2-4x=29$

$=>x^2-4x-29=0$

$=>(x^2-4x+4)-33=0$

$=>(x-2)^2-(\sqrt{33})^2=0$

$=>(x-2-\sqrt{33})(x-2+\sqrt{33})=0$

\(=>\left[{}\begin{matrix}x-2-\sqrt{33}=0=>x=\sqrt{33}+2\\x-2+\sqrt{33}=0=>x=2-\sqrt{33}\end{matrix}\right.\)

Answer 2

[qwerty]

Bài 1:

a) \(\left(5-2x\right)^2-16=0\) (1)

\(\Leftrightarrow\left(5-2x\right)^2=16\)

\(\Leftrightarrow5-2x=\pm4\)

\(\Leftrightarrow\left[{}\begin{matrix}5-2x=4\\5-2x=-4\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{1}{2}\\x=\dfrac{9}{2}\end{matrix}\right.\)

Vậy tập nghiệm phương trình (1) là \(S=\left\{\dfrac{1}{2};\dfrac{9}{2}\right\}\)

b) \(x^2-4x=29\) (2)

\(\Leftrightarrow x^2-4x-29=0\)

\(\Leftrightarrow x=\dfrac{4\pm2\sqrt{33}}{2}\)

\(\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{4+2\sqrt{33}}{2}\\x=\dfrac{4-2\sqrt{33}}{2}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=2+\sqrt{33}\\x=2-\sqrt{33}\end{matrix}\right.\)

Vậy tập nghiệm phương trình (2) là \(S=\left\{2-\sqrt{33};2+\sqrt{33}\right\}\)

c) \(\left(x-3\right)^3-\left(x-3\right)\left(x^2+3x+9\right)+9\left(x+1\right)^2=15\) (3)

\(\Leftrightarrow x^3-9x^2+27x-27-\left(x^3-27\right)+9\left(x^2+2x+1\right)=15\)

\(\Leftrightarrow x^3-9x^2+27x-27-\left(x^3-27\right)+9x^2+18x+9=15\)

\(\Leftrightarrow x^3+27x-27-x^3+27+18x+9=15\)

\(\Leftrightarrow45x+9=15\)

\(\Leftrightarrow45x=15-9\)

\(\Leftrightarrow45x=6\)

\(\Leftrightarrow x=\dfrac{2}{15}\)

Vậy tập nghiệm phương trình (3) là \(S=\left\{\dfrac{2}{15}\right\}\)

d) \(2\left(x-5\right)\left(x+5\right)-\left(x+2\right)\left(2x-3\right)+x\left(x^2+8\right)=\left(x+1\right)\left(x^2-x+1\right)\)(4)

\(\Leftrightarrow2\left(x^2-25\right)-\left(2x^2-3x+4x-6\right)+x^3-8x=x^3+1\)

\(\Leftrightarrow2x^2-50-\left(2x^2+x-6\right)+x^3-8x=x^3+1\)

\(\Leftrightarrow2x^2-50-2x^2-x+6-8x=1\)

\(\Leftrightarrow-44-9x=1\)

\(\Leftrightarrow-9x=1+45\)

\(\Leftrightarrow-9x=45\)

\(\Leftrightarrow x=-5\)

Vậy tập nghiệm phương trình (4) là \(S=\left\{-5\right\}\)