Question

Determinați numărul natural x care verifica egalitatea : a) x^2:2^2=(3^2)^2
B) 25^2-x^2=24^2
C)x:10^3=10^2
D)144:x=3^3
E)3^2+x^2=5^2
F)324:5^x=(3^2*2)^2

Answer 1

Răspuns:

a)x^2 : 2^2 = (3^2)^2

x^2 : 4 = 81

x^2=324

x=18

b) 25^2 - x = 24^2

25-x^2 = 576

x^2= 49

x=7

c) x : 10^3 * 10^2

x=10^3 * 10^2

x=10^5

d)144 : x = 3^3

x=144 supra 27

x= 3,(8)

e)3^2 + x^2=5^2

9+x^2=25

x^2 = 25 - 9

x^2=16

x=4

F) 324:5^x = (3^2*2)^2

324:5^x=324

5^x=324 supra 324

5^x=1

x=0

Answer 2

• a) x² : 2² = (3²)²

x² : 4 = 9²

x² : 4 = 81

x² = 4×81

x² = 324

x = ±18

• b) 25²- x² = 24²

25² - 24² = x²

(25 - 24)(25 + 24) = x²

1×49 = x²

x² = 49

x = ±7

• c) x : 10³ = 10²

x : 1000 = 100

x = 1000×100

x = 100000

• d) 144 : x = 3³

144 : x = 27

x = 144 : 27

x = 144/27

• e) 3² + x² = 5²

9 + x² = 25

x² = 25 - 9

x² = 16

x = ±4