Question

Fie a=1997+1997*1998-1999*1996=.........si b=$[ 2^{12}* 2^{18}+ 25^{65}/ 5^{10}-(3^{25})^2]/[4^{2}*2^{3}* 2^{23}+( 5^{24})^5-(3^{2})^{25}]$
a)Aratati ca a=1999
b)Aratati ca b este patrat perfect

Multumesc anticipat.

Answer 1

a=1997+1997*1998-1999*1996=1997(1+1998)-1999*1996=1997*1999-1999*1996=
=1999(1997-1996)=1999*1=1999

b=[2¹²*2¹⁸+25⁶⁵/5¹⁰-(3²⁵)²] / [4²*2³*2²³+(5²⁴)⁵-(3²)²⁵]=
=[2³⁰+(5²)⁶⁵/5¹⁰-3⁵⁰] / [ 2⁴*2³*2²³+5¹²⁰-3⁵⁰]=
=[2³⁰+5¹³⁰/5¹⁰-3⁵⁰] / [2³⁰+5¹²⁰-3⁵⁰]=
=[2³⁰+5¹²⁰-3⁵⁰] / [2³⁰+5¹²⁰-3⁵⁰]= 1 =1²= patrat perfect