Question

1.Stabiliti valoarea de adevar a urmatoarelor afirmatii:
a) 2x3^2+5^2:5^0+4^2x3-(6^4)^6;2^22:(3^4)^6+5655:435 = 100
b) (2^6)^5x{3^4x28-[3-(2^3x5^3-3^2x10^2-5^2):(1+4)^2]:10^4-2^2^0x3^4] < 2^7x 4^5x3^25.
2. Calculati :
a) 555^3-125x111^3
b) (1+2+2^2+...+2^99):(2^100-1).

Answer 1

a) 2x3²+5²:5⁰+4²x3-(6⁴)⁶: 2²²:(3⁴)⁶+5655:435 = 100 (fals)
2*9+25:1+16*3- (6)²⁴: 2²²: 3²⁴+13=18+25+64-4+13=116

b) (2⁶)⁵x{3⁴x28-[3-(2³x5³-3²x10²-5²):(1+4)²]:10⁴-2²^⁰x3⁴] < 2⁷x 4⁵x3²⁵ (fals)
 =2³⁰x{3⁴x28-[3-(10³- 30²-5²):5²]:10⁴-2x3⁴] =
=2³⁰x[3⁴x28-(3-75:25):10⁴-2x3⁴]=
=2³⁰x[3⁴x28-(3-3):10⁴-2x3⁴]=2³⁰x(3⁴x28-0-2x3⁴)=2³⁰x(3⁴x28-2x3⁴)=
= 2³⁰x3⁴(28-2)=2³⁰x3⁴x26=2³⁰x3⁴x2*13=3³¹x3⁴x13

2.
a) 555³-125x111³= 5³*111³- 5³*111³= 5³*111³ x (1-1)= 0
  b)(1+2+2²+...+2⁹⁹):(2¹⁰⁰-1)= (2¹⁰⁰-1):(2¹⁰⁰-1)=1