Question

1/tìm x

a)x-2 là ước của 3x-13

b)-15.(x-2) + 7.(3-x)=7

c)(2x+1)^2=6

d)4.(5-x)-3.(1-x)=3^2

Answer 1

a) x-2∈ Ư(3x-13)= 3x-13⋮x-2

=3x-6-7⋮x-2=(x-2)(x-2)(x-2)-7⋮x-2

=> x-2∈Ư(-7)={7;1;-7;-1}

Nếu

x-2=7 => x=7+2=> x=9

x-2=1=>x=1+2=>x=3

x-2=-7=>x=(-7)+2=>x=-5

x-2=-1=>x=(-1)+2=>x=1

Vậy x ∈ {9;3;-5;1}

Answer 2

b) \(-15\left(x-2\right)+7\left(3-x\right)=7\)

\(\Leftrightarrow-15x+30+21-7x=7\\ \Leftrightarrow-22x+51=7\\ \Leftrightarrow-22x=7-51\\ \Leftrightarrow-22x=-44\\ \Leftrightarrow x=2\)

Vậy ...

c) \(\left(2x+1\right)^2=6\)

\(\Leftrightarrow4x^2+4x+1=6\\ \Leftrightarrow4x^2+4x+1-6=0\\ \Leftrightarrow4x^2+4x-5=0\\ \Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{\sqrt{6}+1}{2}\\x=\dfrac{\sqrt{6}-1}{2}\end{matrix}\right.\)

Vậy ...

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

\(\Leftrightarrow20-4x-3+3x=9\\ \Leftrightarrow17-x=9\\ \Leftrightarrow-x=9-17\\ \Leftrightarrow-x=-8\\ \Leftrightarrow x=8\)

Vậy ...