Question

1)Se stie ca x-y+2z =5. Calculati suma :
S=(x-y+2z)+(2x-2y+4z) +....+(10x-10y+20z)
2) a) (√12+1) la 2
b) (√3+√2) la 2
c) (√8-3) la 2
d) (√10-√6)la 2
e) (√13-√5)(√13+√5)
f) (5-√6)(5+√6) CINEDA PRIMULSI MAI REPEDE RASPUNSUL ILDAUCACASTIGATOR !!!!!!!!!!!!!!!!!

Answer 1

$1). x-y+2z =5 \\ S=(x-y+2z)+(2x-2y+4z) +...+(10x-10y+20z) \\ S=(x-y+2z)+2(x-y+2z)+...+10(x-y+2z) \\ S=5+2*5+...+10*5 \\ S=5+10+...+50 \\ S=5(1+2+...+10) =5* \frac{10(10+1)}{2} =5* \frac{10*11}{2} = 5* \frac{110}{2} = \\ =5*55=275 \\ S=275 \\ 2a).( \sqrt{12} +1)^2=(2 \sqrt{3} +1)^2=(2 \sqrt{3} )^2+2*2 \sqrt{3} *1+1^2= \\ =12+4 \sqrt{3} +1 =13+4 \sqrt{3} \\ b).( \sqrt{3} + \sqrt{2} )^2= \sqrt{3} ^2+2* \sqrt{3} * \sqrt{2} + \sqrt{2} ^2=3+2 \sqrt{6} +2=5+2 \sqrt{6}$
$c).( \sqrt{8} -3)^2=(2 \sqrt{2} -3)^2=(2 \sqrt{2} )^2-2*2 \sqrt{2} *3+3^2= \\ =8-12 \sqrt{2} +9=17-12 \sqrt{2} \\ d).( \sqrt{10} - \sqrt{6} )^2= \sqrt{10} ^2-2* \sqrt{10} * \sqrt{6} + \sqrt{6} ^2= \\ =10-2 \sqrt{60} +6=16-2 \sqrt{60} =16-2*2 \sqrt{15} =16-4 \sqrt{15} \\ e).( \sqrt{13} - \sqrt{5} )( \sqrt{13} + \sqrt{5} )= 13-5=8 \\ f).(5- \sqrt{6} )(5+ \sqrt{6} )=25-6=19$