Question

(X^2 - 25)+(x - 5)(2x - 11)=0(x^2 - 6x+9)-4=0

Answer 1

\(a,\left(x^2-25\right)+\left(x-5\right)\left(2x-11\right)=0\)

\(\left(x-5\right)\left(x+5\right)+\left(x-5\right)\left(2x-11\right)=0\)

\(\left(x-5\right)\left(x+5+2x-11\right)=0\)

\(\left(x-5\right)\left(3x-6\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-5=0\\3x-6=0\end{cases}\Leftrightarrow}\orbr{\begin{cases}x=5\\x=2\end{cases}}\)

\(b,\left(x^2-6x+9\right)-4=0\)

\(x^2-6x+9-4=0\)

\(x^2+6x+5=0\)

\(x^2+x+5x+5=0\)

\(x\left(x+1\right)+5\left(x+1\right)=0\)

\(\left(x+1\right)\left(x+5\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x+1=0\\x+5=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=-1\\x=-5\end{cases}}}\)

Chúc bạn hok tốt

Answer 2

1. \(\left(x^2-25\right)+\left(x-5\right).\left(2x-11\right)=0\)

\(\Leftrightarrow\)\(\left(x-5\right).\left(x+5\right)+\left(x-5\right).\left(2x-11\right)=0\)

\(\Leftrightarrow\)\(\left(x-5\right).\left(x+5+2x-11\right)=0\)

\(\Leftrightarrow\)\(\left(x-5\right).\left(3x-6\right)=0\)

\(\Leftrightarrow\)\(3.\left(x-5\right).\left(x-2\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x-5=0\\x-2=0\end{cases}}\Rightarrow\orbr{\begin{cases}x=5\\x=2\end{cases}}\)

Answer 3

\(1.\left(x^2-25\right)+\left(x-5\right)\left(2x-11\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+5\right)+\left(x-5\right)\left(2x-11\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(x+5+2x-11\right)=0\)

\(\Leftrightarrow\left(x-5\right)\left(3x-6\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-5=0\\3x-6=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=2\end{cases}}}\)

\(2.\left(x^2-6x+9\right)-4=0\)

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

\(\Leftrightarrow\left(x-5\right)\left(x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-5=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=5\\x=1\end{cases}}}\)

Answer 4

1,\(\Leftrightarrow\)\(^{\left(x^2-25\right)+\left(x-5\right)\left(2x-11\right)=0}\)

\(\Leftrightarrow\)\(\left(x-5\right)\left(x+5\right)+\left(x-5\right)\left(2x-11\right)=0\)

\(\Leftrightarrow\)\(\left(x-5\right)\left(x+5+2x-11\right)=0\)

\(\Leftrightarrow\)\(\left(x-5\right)\left(3x-6\right)=0\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x-5=0\\3x-6=0\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=5\\x=2\end{cases}}\)

vậy x=5 hoặc x=2 là nghiệm của p/t

2

\(x^2-6x+9=4\)

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

\(\Leftrightarrow\)\(\orbr{\begin{cases}x-3=2\\x-3=-2\end{cases}}\)

\(\Leftrightarrow\)\(\orbr{\begin{cases}x=5\\x=1\end{cases}}\)

vậy x=5 và x=1 là nghiệm của p/t