Question

Determina numerele a, b ∈ Q , astfel incat a√2-b=(√2-2)².

Answer 1

[tex]a\sqrt{2}-b=(\sqrt{2}-2)^2\\ a\sqrt2 -b=2-4\sqrt2 +4\\ a\sqrt2+4\sqrt2= b+6\\ \sqrt 2(a+4)=b+6\\ \text{Evident,} b+6\in\mathbb{Q},\text{deci si }\sqrt2(a+4)\text{ trebuie sa apartina lui }\mathbb{Q}\\ \text{Observam ca }\sqrt{2}\in \mathbb{R-Q},\text{prin urmare conditia devine :}\\ a+4=0\Rightarrow a=-4\\ b+6=0\Rightarrow b=-6[/tex]