Răspuns:
[tex] \mathsf{ x = 4}[/tex]
Explicație pas cu pas:
[tex] \mathsf{4x^2 -32x+64=0 } [/tex]
[tex] \mathsf{ 4(x^2 -8x+16)=0 } [/tex]
[tex] \mathsf{ 4[x^2 -4x-4x+16]=0 } [/tex]
[tex] \mathsf{ 4[(x^2 -4x)-(4x-16)]=0 }[/tex]
[tex] \mathsf{ 4[x(x -4)-4(x-4)]=0 }[/tex]
[tex] \mathsf{ 4[(x -4)(x-4)]=0 }[/tex]
[tex] \mathsf{ 4(x -4)^2=0 }[/tex]
[tex] \mathsf{ (x -4)^2 = \frac{0}{4} }[/tex]
[tex] \mathsf{ (x -4)^2 = 0 }[/tex]
[tex] \mathsf{(x -4) = 0}[/tex]
[tex] \mathsf{ x = 4 }[/tex]
Explicație pas cu pas:
[tex]4x^{2} - 32x+64=0 \\ \\ 4( {x}^{2} - 8x + 16) = 0 \\ \\ 4( {x}^{2} - 4x - 4x + 16) = 0 \\ \\ 4(x(x - 4) - 4(x - 4)) = 0 \\ \\ 4((x - 4)(x - 4)) = 0 \\ \\ 4(x - 4)^{2} = 0 \\ \\ (x - 4)^{2} = 0 \\ \\ x - 4 = 0 \\ \\ \boxed{x = 4}[/tex]
