Question

${2}^{ {x}^{2} + 2x} \times {3}^{ {x}^{2} + 2x } = {216}^{x + 2}$

Answer 1

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Answer 2

${2}^{ {x}^{2} + 2x} \cdot {3}^{ {x}^{2} + 2x } = {216}^{x + 2}$

$6^{ {x}^{2} + 2x } = (6^3)^{x + 2}$

$6^{ {x}^{2} + 2x } = 6^{3(x + 2)}$

$x^2 + 2x=3x+6$

$x^2+2x-3x-6=0$

$x^2-x-6=0$

$D=(-1)^2-4 \cdot 1 \cdot (-6)=1+24=25$

$\sqrt{D} = \sqrt{25}=5$

$x_1= \frac{1-5}{2}= \frac{-4}{2} =-2$

$x_2= \frac{1+5}{2}= \frac{6}{2} =3$