Question

Efectuati:
a)Aratati ca nr naturale x si y sunt patrate perfecte.
x=[2^30^2x(2^6)^100x2+(64^4)^100:2^899]^2+2^3007
y=5x(3^2002-3^3001-9^1000
b) (4^31+6X32^12-5X16^15):(8^21-5X8^20)-1

Answer 1

x=[2³⁰^²x(2⁶)¹⁰⁰*2+(64⁴)¹⁰⁰:2⁸⁹⁹]^2+2³⁰⁰⁷=
=(2⁹⁰⁰*2⁶⁰⁰*2+2²⁴⁰⁰:2⁸⁹⁹)²+2³⁰⁰⁷=
=(2¹⁵⁰¹+2¹⁵⁰¹)²+2³⁰⁰⁷=
=(2*2¹⁵⁰¹)²+2³⁰⁰⁷=
=2¹⁵⁰²*²+2³⁰⁰⁷=
=2³⁰⁰⁴+2³⁰⁰⁷=
=2³⁰⁰⁴(1+2³)=
=2³⁰⁰⁴*9=2¹⁵⁰²*² * 3²=
=(2¹⁵⁰²*3)²

y=5*(3²⁰⁰²-3²⁰⁰¹-9¹⁰⁰⁰)=
=5*(3²⁰⁰²-3²⁰⁰¹-3²⁰⁰⁰)=
=5*3²⁰⁰⁰(3²-3-1)=
=5*3²⁰⁰⁰*5=5²*3¹⁰⁰⁰*²=
=(5*3¹⁰⁰⁰)²

b) (4³¹+6*32¹²-5*16¹⁵):(8²¹-5*8²⁰)-1=
=(2⁶²+3*2*2⁵*¹²-5*2⁴*¹⁵):(2³*²¹-5*2³*²⁰)-1=
=(2⁶²+3*2⁶¹-5*2⁶⁰):(2⁶³-5*2⁶⁰)-1=
=2⁶⁰(2²+6-5):2⁶⁰(2³-5)-1=
=5:3-1=5/3-3/3=2/3