Question

A equação 2x² -12x + 9 = 0 possui apenas uma raiz, qual é? *

Answer 1

Resposta:

$x_{1} = \frac{6+3\sqrt{2} }{2} \\x_{2} = \frac{6-3\sqrt{2} }{2}$

Explicação passo-a-passo:

Resolvendo

Δ = $b^{2} -4ac$ =>$(-12)^{2} -4(2)(9) => 144^{} - 72 => 72$ Δ = 72

X = $\frac{ -(-12) ± \sqrt{72} }{2.2}$ => $\frac{12 +\sqrt{72} ^{} }{4}=> \frac{12 +\sqrt{36.2} ^{} }{4} => \frac{12 +6\sqrt{.2} ^{} }{4}=> \frac{12:2 +6:2\sqrt{.2} ^{} }{4:2}=> x_{1} \frac{6 +3\sqrt{.2} ^{} }{2}$

X = $\frac{ -(-12) ± \sqrt{72} }{2.2}$ => $\frac{12 -\sqrt{72} ^{} }{4}=> \frac{12 -\sqrt{36.2} ^{} }{4} => \frac{12 - 6\sqrt{.2} ^{} }{4}=> \frac{12:2 -6:2\sqrt{.2} ^{} }{4:2}=> x_{2} \frac{6 -3\sqrt{.2} ^{} }{2}$