Question

Cum se rezolva ecuatia 2^(x^2+1)=2√2?​

Answer 1

${2}^{ {x}^{2} + 1 } = 2 \sqrt{2}$

${2}^{ {x}^{2} + 1 } = 2 \times {2}^{ \frac{1}{2} }$

${2}^{ {x}^{2} + 1 } = {2}^{1 + \frac{1}{2} }$

${2}^{ {x}^{2} + 1 } = {2}^{ \frac{3}{2} }$

${x}^{2} + 1 = \frac{3}{2}$

${x}^{2} = \frac{3}{2} - 1$

${x}^{2} = \frac{1}{2}$

$x = \pm \sqrt{ \frac{1}{2} }$

$x = \pm \frac{ \sqrt{1} }{ \sqrt{2} }$

$x = \pm \frac{1}{ \sqrt{2} }$

$x = \pm \frac{ \sqrt{2} }{2}$

Answer 2

Răspuns:

scriind radicalul ca putere fractionara

Explicație pas cu pas:

2^(x²+1) =2^1*2^(1/2)

x²+1=3/2

x²=1/2

x=+-1/√2=+-√2/2

S= {-√2/2;√2/2} care verifica ecuatia