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\(63x^2-16x+1=0\)
\(\Leftrightarrow63x^2-9x-7x+1=0\)
\(\Leftrightarrow9x\left(7x-1\right)-\left(7x-1\right)=0\)
\(\Leftrightarrow\left(9x-1\right)\left(7x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}9x-1=0\\7x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=\frac{1}{9}\\x=\frac{1}{7}\end{cases}}}\)
Bài làm:
Ta có: \(63x^2-16x+1=0\)
\(\Leftrightarrow\left(63x^2-9x\right)-\left(7x-1\right)=0\)
\(\Leftrightarrow9x\left(7x-1\right)-\left(7x-1\right)=0\)
\(\Leftrightarrow\left(7x-1\right)\left(9x-1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}7x-1=0\\9x-1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=\frac{1}{9}\\x=\frac{1}{7}\end{cases}}\)
\(63x^2-65x-8=0\)
Ta có: \(\Delta=65^2+4.8.63=6241\)
Vậy pt có 2 nghiệm:
\(x_1=\frac{65+\sqrt{6241}}{126}\);\(x_2=\frac{65-\sqrt{6241}}{126}\)
\(63x^2-65x-8=0\)
\(63x^2-72x+7x-8=0\)
\(9x\cdot\left(7x-8\right)+7x-8=0\)
\(\left(7x-8\right)\cdot\left(9x+1\right)=0\)
\(\orbr{\begin{cases}7x-8=0\\9x+1=0\end{cases}\Rightarrow\orbr{\begin{cases}x=\frac{8}{7}\\x=-\frac{1}{9}\end{cases}}}\)
\(16x^3-16x^4+4x-8x^2-1=0\)
<=> \(-16x^4-4x^2+16x^3+4x-4x^2-1=0\)
<=> \(-4x^2\left(4x+1\right)+4x\left(4x^2+1\right)-\left(4x^2+1\right)=0\)
<=> \(-\left(4x^2+1\right)\left(4x^2-4x+1\right)=0\)
<=> \(-\left(4x^2+1\right)\left(2x-1\right)^2=0\)
<=> \(2x-1=0\) (do 4x2 + 1 > 0 )
<=> \(x=\frac{1}{2}\)
a) \(x^3-16x=0\)
\(\Leftrightarrow x\left(x^2-16\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}x=0\\x^2-16=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=0\\x=\pm\sqrt{16}=\pm4\end{cases}}\)
Vậy \(x\in\left\{0;\pm4\right\}\)
b) \(x^2-6x+9=0\)
\(\Leftrightarrow\left(x-3\right)^2=0\)
\(\Leftrightarrow x-3=0\)
\(\Leftrightarrow x=3\)
a) \(7x^2-16x=2x^3-56\)
\(\Leftrightarrow\)\(2x^3-7x^2+16x-56=0\)
\(\Leftrightarrow\)\(2x\left(x^2+8\right)-7\left(x^2+8\right)=0\)
\(\Leftrightarrow\)\(\left(2x-7\right)\left(x^2+8\right)=0\)
\(\Leftrightarrow\)\(2x-7=0\)
\(\Leftrightarrow\)\(x=3,5\)
Vậy...
b) \(x^7+x^3+2x^5+2x=0\)
\(\Leftrightarrow\)\(x.\left(x^6+x^2+2x^4+2\right)=0\)
\(\Leftrightarrow\)\(x\left(x^2+2\right)\left(x^4+1\right)=0\)
\(\Leftrightarrow\)\(x=0\)
Vậy...
c) \(\left(2x+1\right)x-5\left(x+\frac{1}{2}\right)=0\)
\(\Leftrightarrow\)\(2x\left(x+\frac{1}{2}\right)-5\left(x+\frac{1}{2}\right)=0\)
\(\Leftrightarrow\)\(\left(2x-5\right)\left(x+\frac{1}{2}\right)=0\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}2x-5=0\\x+\frac{1}{2}=0\end{cases}}\)
\(\Leftrightarrow\)\(\orbr{\begin{cases}x=2,5\\x=-0,5\end{cases}}\)
Vậy...
Ta có : 63x2 + 16x + 1 = 0
=> 63x2 + 9x + 7x + 1 = 0
=> 9x(7x + 1) + (7x + 1) = 0
=> (9x + 1)(7x + 1) = 0
=> \(\orbr{\begin{cases}9x+1=0\\7x+1=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=-\frac{1}{9}\\x=-\frac{1}{7}\end{cases}}\)
Vậy \(x\in\left\{-\frac{1}{9};-\frac{1}{7}\right\}\)
\(63x^2+16x+1=0\)
\(\Leftrightarrow63x^2+7x+9x+1=0\)
\(\Leftrightarrow7x\left(9x+1\right)+\left(9x+1\right)=0\)
\(\Leftrightarrow\left(7x+1\right)\left(9x+1\right)=0\)
\(\Leftrightarrow\orbr{\begin{cases}7x+1=0\\9x+1=0\end{cases}}\Leftrightarrow\orbr{\begin{cases}x=-\frac{1}{7}\\x=-\frac{1}{9}\end{cases}}\)