Question

a) x²  - 7 = 0       

b) ( x - 1 )² = 4         

c) ( 3x - 2 ) ( 4x + 5 ) = 0   

d) ( x - 4 )² - ( x + 2 ) ( x - 6 ) = 0             

e) 4x² - 1 = ( 2x + 1 ) ( 3x - 5 )

Answer 1

Answer 2

`a) x^2-7=0`

`=>x^2=7`

`=>x=7^2`

`=>x=`\(\pm7\)

`b)(x-1)^2=4`

`=>x-1=2`

`=>x=2+1`

`=>x=3`

`c)(3x-2)(4x+5)=0`

\(\Rightarrow\left[{}\begin{matrix}3x-2=0\Rightarrow x=\dfrac{2}{3}\\\\4x+5=0\Rightarrow x=\dfrac{-5}{4}\end{matrix}\right.\)

`=>x={2/3;(-5)/4}`

`d)(x-4)^2 -(x+2)(x-6)=0`

`=>x^2 -8+16 -x^2+6x-2x+12=0`

`=>20+4x=0`

`=>4x=-20`

`=>x=(-20)/4`

`=>x=-5`

`e)4x^2 -1=( 2x + 1 ) ( 3x - 5 )`

`=>4x^2-1=6x^2-10x+3x-5`

`=>4x^2-1=6x^2-7x-5`

`=>4x^2-1-6x^2+7x+5=0`

`=>-2x^2+7x+4=0`

`=>(x-4)(x+1/2)=0`

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\Rightarrow x=4\\x+\dfrac{1}{2}=0\Rightarrow x=\dfrac{-1}{2}\end{matrix}\right.\)