Question

Dacă x+y+z=17…, calculați:
a) 5•x+5•y+5•z=
b)13•x+13•y+13•z -1313
c) 882- 3• (7 •x + 7•y + 7•z) =
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Identificând un factor comun, în fiecare sumă, calculați:

b) 10+20+30+...+1230=
c)7+14+21+...+315=

P.s - Vă mulțumesc pentru timpul acordat acestor probleme !

Answer 1

a) 5(x+y+z)=5·17=85
b) 13(x+y+z)-1313=13·17-13·13=221-169=52 sau ptc nu am inteles la urma
=221-1313=-1092
c) 882-3·7(x+y+z)=882-21·17=882-357=525

b) 10(1+2+3+....123)
folosind suma lui gauss rezulta1+2+...n=n(n+1)/2
10·123(123+1)/2=1230·124/2=76260
c) 7(1+2+3+...+45)=7·45(45+1)/2=315·46/2=7245

Answer 2

$1).x+y+z=17 \\ a).5x+5y+5z=5(x+y+z)=5 \cdot 17=85 \\ b).13x+13y+13x-1313=13(x+y+z)-1313= \\ =13 \cdot 17-1313=221-1313=-1092 \\ c).882-3(7x+7y+7z)=882-3 \cdot 7(x+y+z)= \\ =882-3 \cdot 7 \cdot 17=882-21 \cdot 17=882-357=525$
$\displaystyle 2a).10+20+30+...+1230=10(1+2+3+...+123)= \\ \\ =10 \times \frac{123 (123+1)}{2} =10 \times \frac{123 \times 124}{2} = 10 \times \frac{15252}{2} = \\ \\ =10 \times 7627=76260 \\ \\ b).7+14+21+...+315=7(1+2+3+...+45)=7 \times \frac{45(45+1)}{2} = \\ \\ =7 \times \frac{45\times 46}{2} =7 \times \frac{2070}{2} =7 \times 1035=7245$