Question

1_ (√5-4)² :

2_ (√2-√3)² :

3_ (√2-5)² :

Alluda por favor​

Answer 1

Respuesta:

$\left(\sqrt{5}-4\right)^2=21-8\sqrt{5}\quad \left(\mathrm{Decimal:\quad }\:3.11145\dots \right)\\\left(\sqrt{2}-\sqrt{3}\right)^2=5-2\sqrt{6}\quad \left(\mathrm{Decimal:\quad }\:0.10102\dots \right)\\\left(\sqrt{2}-5\right)^2=27-10\sqrt{2}\quad \left(\mathrm{Decimal:\quad }\:12.85786\dots \right)$

Explicación paso a paso:

$\left(\sqrt{5}-4\right)^2\\=\left(\sqrt{5}\right)^2-2\sqrt{5}\cdot \:4+4^2\\=21-8\sqrt{5}\\\\\left(\sqrt{2}-\sqrt{3}\right)^2\\=\left(\sqrt{2}\right)^2-2\sqrt{2}\sqrt{3}+\left(\sqrt{3}\right)^2\\=5-2\sqrt{6}\\\\\left(\sqrt{2}-5\right)^2\\=\left(\sqrt{2}\right)^2-2\sqrt{2}\cdot \:5+5^2\\=27-10\sqrt{2}$