Question

Realizar las siguientes ecuaciones y calculos combinados
a) x + 25 - 32 : 4 = 32
b) 45 - 3 . 2 = x - √16 + 3³ : 9
c) x . 4 - 40 . 2 = 66 : 11 + ∛8
d) x : √4 - 3⁴ . 2 = 140 : 2 + 15 : 3
e) [(9-2)² + (2+5-3)² + √81 : ∛729] . ∛27 - (√102 + 3⁴)=
f) (6² + √49 . ∛8 - [4² - (10² + 2²) : (√144 + 1)] . ∛1000 - √36=

Answer 1

$a) \ x+25-32:4=32 \\ x+25-8=32 \\ x+17=32 \\ x=15 \\ b) \ 45-3 \cdot 2=x-\sqrt{16}+3^{3}:9 \\ 45-6=x-4+27:9 \\ 39=x-4+3 \\ 39=x-1 \\ x=40 \\ c) \ x \cdot 4-40 \cdot 2=66:11+\sqrt[3]{8} \\ 4x-80=6+2 \\ 4x-80=8 \\ 4x=88 \qquad /:4 \\ x=22$
$d) x:\sqrt{4}-3^{4} \cdot 2=140:2+15:3 \\ x:2-81 \cdot 2=70+5 \\ x:2-162=75 \\ x:2=237 \qquad /\cdot 2 \\ x=474 \\ e) \ [(9-2)^{2}+(2+5-3)^{2}+\sqrt{81}:\sqrt[3]{729}] \cdot \sqrt[3]{27}-(\sqrt{102}+3^{4})= \\ =(7^{2}+4^{2}+9:9) \cdot 3-\sqrt{102}+81=(49+16+1) \cdot 3-\sqrt{102}+81= \\ =66 \cdot 3-\sqrt{102}+81=198+81-\sqrt{102}=289-\sqrt{102}$
$f) \ (6^{2}+\sqrt{49} \cdot \sqrt[3]{8}-[4^{2}-(10^{2}+2^{2}):(\sqrt{144}+1)]) \cdot \sqrt[3]{1000}-\sqrt{36}= \\ =(36+7 \cdot 2-(16-(100+4):(12+1)) \cdot 10-6= \\ =(36+14-(16-8)) \cdot 10-6=(50-8) \cdot 10-6=42 \cdot 10-6= \\ =420-6=414$