Question

desenvolva os seguintes produtos notáveis:
a) (√3 + 1)².
b) (3- √2)²
c) (√5 + √2)²
d) (√11 + √2)• (√11 - √2)
e) ( ⁴√3 + 1)².
f) (2 + √2)³​

Answer 1

Olá!!!

Resposta...

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$\tt =\left(\sqrt{3}+1\right)^2$

$\tt =\left(\sqrt{3}\right)^2+2\sqrt{3}\cdot \:1+1^2$

$\tt =4+2\sqrt{3}$

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$\tt =\left(3-\sqrt{2}\right)^2$

$\tt =3^2-2\cdot \:3\sqrt{2}+\left(\sqrt{2}\right)^2$

$\tt =11-6\sqrt{2}$

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$\tt =\left(\sqrt{5}+\sqrt{2}\right)^2$

$\tt =\left(\sqrt{5}\right)^2+2\sqrt{5}\sqrt{2}+\left(\sqrt{2}\right)^2$

$\tt =7+2\sqrt{10}$

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$\tt =\left(\sqrt{11}+\sqrt{2}\right)\left(\sqrt{11}-\sqrt{2}\right)$

$\tt =\left(\sqrt{11}\right)^2-\left(\sqrt{2}\right)^2$

$\tt =9$

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$\tt =\left(4\sqrt{3}+1\right)^2$

$\tt =\left(4\sqrt{3}\right)^2+2\cdot \:4\sqrt{3}\cdot \:1+1^2$

$\tt =49+8\sqrt{3}$

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$\tt = \left(2+\sqrt{2}\right)^3$

$\tt =2^3+3\cdot \:2^2\sqrt{2}+3\cdot \:2\left(\sqrt{2}\right)^2+\left(\sqrt{2}\right)^3$

$\tt =20+14\sqrt{2}$