Question

(2+raiz de 5) × ( raiz de 9-4×raiz de 5)

Answer 1

Explicação passo-a-passo:

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Answer 2

Resposta:

Explicação passo-a-passo:

$\left(2+\sqrt{5}\right)\cdot \left(\sqrt{9}-4+\sqrt{5}\right)\\ \sqrt{9}=3\\ \mathrm{Fatorar\:o\:numero:\:}\:9=3^2\sqrt{3^2}\\ \mathrm{Aplicar\:as\:propriedades\:dos\:radicais}:\quad \sqrt[n]{a^n}=a\\ \sqrt{3^2}=3\\ =3\\ =\left(2+\sqrt{5}\right)\left(3+\sqrt{5}-4\right)\\ \mathrm{Subtrair:}\:3-4=-1\\ \left(2+\sqrt{5}\right)\left(\sqrt{5}-1\right)\\ \mathrm{Aplicar\:metodo\:FOIL}:\quad \left(a+b\right)\left(c+d\right)=ac+ad+bc+bd\\ a=2,\:b=\sqrt{5},\:c=\sqrt{5},\:d=-1$

$=2\sqrt{5}+2\left(-1\right)+\sqrt{5}\sqrt{5}+\sqrt{5}\left(-1\right)\\ \mathrm{Aplicar\:as\:regras\:dos\:sinais}\\ +\left(-a\right)=-a\\ =2\sqrt{5}-2\cdot \:1+\sqrt{5}\sqrt{5}-1\cdot \sqrt{5}\\ \mathrm{Simplificar}\:2\sqrt{5}-2\cdot \:1+\sqrt{5}\sqrt{5}-1\cdot \sqrt{5}:\quad 3+\sqrt{5}\\ 2\sqrt{5}-2\cdot \:1+\sqrt{5}\sqrt{5}-1\cdot \sqrt{5}\\ \mathrm{Somar\:elementos\:similares:}\:2\sqrt{5}-1\cdot \sqrt{5}=\sqrt{5}\\ =\sqrt{5}-2\cdot \:1+\sqrt{5}\sqrt{5}\\ \mathrm{Multiplicar\:os\:numeros:}\:2\cdot \:1=2$

$=\sqrt{5}-2+\sqrt{5}\sqrt{5}\\ \mathrm{Aplicar\:as\:propriedades\:dos\:radicais}:\quad \sqrt{a}\sqrt{a}=a\\ \sqrt{5}\sqrt{5}=5\\ =\sqrt{5}-2+5\\ \mathrm{Somar/subtrair:}\:-2+5=3\\ =3+\sqrt{5}$

A resposta é $=3+\sqrt{5}$