Question

Se consideră expresia ​

Answer 1

Explicație pas cu pas:

a)

${x}^{2} + 3x \sqrt{2} + 4 = \\ = {x}^{2} + x \sqrt{2} + 2x \sqrt{2} + {2} \sqrt{2} \sqrt{2} \\ = x(x + \sqrt{2}) + 2 \sqrt{2} (x + \sqrt{2}) \\ = (x + \sqrt{2} )(x + 2 \sqrt{2})$

b)

$E(x)=x - (1+\frac{ \sqrt{18}}{x-2 \sqrt{2} })\div (\frac{ {x}^{2}+3x \sqrt{2}+4}{ {x}^{2} - 8}) = x - \frac{x - 2 \sqrt{2} + 3\sqrt{2}}{x - 2 \sqrt{2}} \times \frac{(x - 2 \sqrt{2} )(x + 2 \sqrt{2}) }{(x + \sqrt{2})(x + 2 \sqrt{2} ) }=x - \frac{x + \sqrt{2} }{x + \sqrt{2} } = x - 1$