Question

ex 27 vă rog 8/2- radical din 2 - 4 radical din doi = 8​

Answer 1

 

$\displaystyle\bf\\\frac{8}{2-\sqrt{2}}-4\sqrt{2}=8\\\\\textbf{N-ai scris ce se cere, dar presupun ca trebuie sa aratam}\\\textbf{ca expresia din stanga egalului este egala cu 8}\\\\\frac{8}{2-\sqrt{2}}-4\sqrt{2}=~~~(Rationalizam~fractia.)\\\\\\=\frac{8(2+\sqrt{2})}{(2-\sqrt{2})(2+\sqrt{2})}-4\sqrt{2}=\\\\\\=\frac{16+8\sqrt{2}}{4-2}-4\sqrt{2}=\\\\\\=\frac{16+8\sqrt{2}}{2}-4\sqrt{2}=\\\\=8+4\sqrt{2}-4\sqrt{2}=8\\cctd$

 

 

Answer 2

"8/2- radical din 2 - 4 radical din doi = 8"

8/(2-√2) - 4√2 = 8

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$\it \dfrac{8}{2-\sqrt2}-4\sqrt2=8|_{:8} \Leftrightarrow \dfrac{1}{2-\sqrt2}-\dfrac{\sqrt2}{2}=1\Big|_{+\dfrac{\sqrt2}{2}} \Leftrightarrow \dfrac{1}{2-\sqrt2}=\dfrac{2+\sqrt2}{2} \Leftrightarrow \\ \\ \\ \Leftrightarrow 2\cdot1=(2+\sqrt2)(2-\sqrt2) \Leftrightarrow 2=4-2\sqrt2+2\sqrt2-2 \Leftrightarrow 2=2\ (A)$