Question

conjunto solução da equação X^2 - 14x + 42 = 0 no Conjunto R

Answer 1

$x {}^{2} - 14x + 42 = 0$

$x = \dfrac{ - ( - 14) \dfrac{ + }{} \sqrt{( - 14) {}^{2} - 4 \times 1 \times 42 } }{2 \times 1}$

$x = \dfrac{14 \dfrac{ + }{} \sqrt{196 - 168} }{2}$

$x = \dfrac{14 \dfrac{ + }{} \sqrt{28} }{2}$

$x = \dfrac{14 \dfrac{ + }{} \sqrt{2 {}^{2} \times 7 } }{2}$

$x = \dfrac{14 \dfrac{ + }{} \sqrt{2 {}^{2} } \sqrt{7} }{2}$

$x = \dfrac{14 \frac{ + }{}2 \sqrt{7} }{2}$

$x {}^{1} = \dfrac{14 + 2 \sqrt{7} }{2}$

$x {}^{1} = \dfrac{2(7 + \sqrt{7}) }{2}$

Reduzindo

$x {}^{1} = 7 + \sqrt{7}$

$x {}^{2} = \dfrac{14 - 2 \sqrt{7} }{2}$

$x {}^{2} = \dfrac{2(7 - \sqrt{7} )}{2}$

Reduzindo

$x {}^{2} = 7 - \sqrt{7}$