Question

calcule : (√201 + √199 . (√201 - √199)

Answer 1

(a + b)² = a² + 2ab + b² 

(√201+√199) * (√201+√199) = (√201+√199)² 

(√201+√199)² = (√201² + 2*√201*√199 + √199²) = 

( 201 + 199 + 2*√201*√199) = 400 + 2*√[(200+1)(200-1)] = 

400 + 2*√(200² - 1) = 400 + 399.995 ~ 800

Answer 2

Resposta:

$\left(\sqrt{201}+\sqrt{199}\right)\left(\sqrt{201}-\sqrt{199}\right)\\\\\mathrm{Aplicar\:a\:regra\:da\:diferenca\:de\:quadrados:\:}\left(a+b\right)\left(a-b\right)=a^2-b^2\\\\\left(\sqrt{201}\right)^2-\left(\sqrt{199}\right)^2\\\\\left(\sqrt{201}\right)^2-\left(\sqrt{199}\right)^2=2\\\\=2$