Question

1.Tìm X thuộc Z biết:

a.(-4).\(\left(x-2\right)^2=-100\)

b.3.(2.X+8)-(5.X+2)=0

c. 5.(7-3.X)+7.(2+2.X)=0

2.CM các đẳng thức sau:

a) x.(y+z)-y.(x-z)=(x+y).z

b) x.(y-z)-x.(y+a)= -x.(z+a)

Answer 1

a/ \(\left(-4\right)\left(x-2\right)^2=-100\)

\(\Leftrightarrow\left(x-2\right)^2=\left(-100\right):\left(-4\right)\)

\(\Leftrightarrow\left(x-2\right)^2=25\)

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

\(\Leftrightarrow\left[{}\begin{matrix}x=7\\x=-3\end{matrix}\right.\)

Vậy ...

b/ \(3\left(2x+8\right)-\left(5x+2\right)=0\)

\(\Leftrightarrow6x+24=5x+2\)

\(\Leftrightarrow6x-5x=2-24\)

\(\Leftrightarrow x=-22\)

Vậy ....

c/ \(5\left(7-3x\right)+7\left(2+2x\right)=0\)

\(\Leftrightarrow5\left(7-3x\right)=-7\left(2+2x\right)\)

\(\Leftrightarrow35-15x=-14+\left(-14\right)x\)

\(\Leftrightarrow35+14=\left(-14\right)x+15x\)

\(\Leftrightarrow x=49\)

Vậy ....