Răspuns:
[tex]x = ( - 2 - \sqrt{3} \: ; \: \sqrt{3} )[/tex]
Explicație pas cu pas:
[tex]12(x + 1) {}^{2} = (6 + 2 \sqrt{3} ) {}^{2} [/tex]
[tex]12( {x}^{2} + 2x + 1) = 36 + 24 \sqrt{3} + 12[/tex]
[tex]12 {x}^{2} + 24x + 12 = 36 + 24 \sqrt{3} + 12[/tex]
[tex]12 {x}^{2} + 24x = 36 + 24 \sqrt{3} [/tex]
[tex]12 {x}^{2} + 24x - 36 - 24 \sqrt{3} = 0[/tex]
[tex]x {}^{2} + 2x - 3 - 2 \sqrt{3} = 0[/tex]
[tex]x = \frac{ - 2± \sqrt{ {2}^{2} - 4 \times 1( - 3 - 2 \sqrt{3} } )}{2 \times 1} [/tex]
[tex]x = \frac{ - 2± \sqrt{ {2}^{2} + 8 \sqrt{3} + 12 } }{2} [/tex]
[tex]x = \frac{ - 2±2 + 2 \sqrt{3} }{2} [/tex]
[tex]x = \frac{ - 2 + 2 + 2 \sqrt{3} }{2} = > x = \frac{2 \sqrt{3} }{2} = \sqrt{3} [/tex]
[tex]x = \frac{ - 2 - (2 + 2 \sqrt{3} )}{2} = > x = \frac{2 ( - 2 - \sqrt{3}) }{2} = - 2 - \sqrt{3} [/tex]
[tex] = > x = ( - 2 - \sqrt{3} \: ; \: \sqrt{3} )[/tex]
(a + b)² = a² + 2ab + b²
[tex]x = \frac{ - b± \sqrt{ {b}^{2} - 4ac} }{2a} [/tex]
a² + 2ab + b² = (a + b)²
