Question

PRECISO DE AJUDA PFVR!!
Se:
A=(√5-10).(√5+ √10)
B=(3√3-2√3)²
C=(5√7+3 √2).(5 √7-3 √2)
D=(5-3 √2).(5+3 √2)
E=(2³√3)³
Então, A+B+C+D+E, será:
A)186
B)191
C)196
D)198
E)201

Answer 1

Resposta:

ツ

Alternativa D

Explicação passo a passo:

Calcularemos o valor de cada letra:

$A=(\sqrt{5}-\sqrt{10}).(\sqrt{5}+\sqrt{10} )\\A=\sqrt{25} +\sqrt{50}-\sqrt{50}-\sqrt{100} \\A=5-10\\\boxed{A=-5}$

$B=(3\sqrt{3}-2\sqrt{3})^{2}\\B=(\sqrt{3} )^{2}\\\boxed{B=3}$

$C=(5\sqrt{7}+3\sqrt{2}).(5\sqrt{7}-3\sqrt{2})\\C=25\sqrt{49} -15\sqrt{14}+15\sqrt{14}-9\sqrt{4} \\C=25.7-3.2\\C=175-6\\\boxed{C=169}$

$D=(5-3\sqrt{2}).(5+3\sqrt{2})\\D=25+15\sqrt{2}-15\sqrt{2}-9\sqrt{4} \\D=25-9.2\\D=25-18\\\boxed{D=7}$

$E=(2\sqrt[3]3} )^{3}\\E=(2)^{3}.(\sqrt[3]3} )^{3}\\E=8.3\\\boxed{E=24}$

Agora basta somar A + B + C + D + E:

$(-5) + (3) + (169) + (7) + (24)=-5+203=\boxed{\boxed{198}}$