Question

Arătați că următoarele numere sunt patrate perfecte a) 17^28 b) 25^19 c) 1+3+5+7+...+55

Answer 1

$a) {17}^{28} = {17}^{14 \times 2} = { ({17}^{14} )}^{2} = > p.p$

$b) {25}^{19} = {( {5}^{2} )}^{19} = { ({5}^{19} )}^{2} = > p.p$

$c)1 + 3 + 5 + 7 + ... + 55$

$1 + 3 + 5 + 7 + ... + 2n - 1 = {n}^{2}$

$2n - 1 = 55$

$2n = 55 + 1$

$2n = 56 \: | \div 2$

$n = 28$

${n}^{2} = {28}^{2} = > p.p$

Answer 2

a) 17^28=(17^14)^2=>p.p

b) 25^19=(5^2)^19=(5^19)^2=>p.p

c) 1+3+5+...+2n-1=n^2

2n-1=55

2n=55+1

2n=56

n=56/2

n=28

n^2=28^2=>p.p