Question

1.Fie a,b,c,d ∈R, asfel incat a+b=20 si c+d=30.Calculatii ac+ad+bc+bd.
2.Fie x,y∈R,x≠0,asfel incat 2 supra x=y supra3.Calculati(xy-7) totul ,la 100.
3.Fie a,b,c trei numere reale , asfel incat a+b=20,b+c=30,c+a=40.
a)Calcultii a+b+c.
b)Aflati valoarea luia.
4.Rezolvatii ecuatiile:
a)3x+1 supra √5=x+42 supra√20,x∈R
b)(y+2)²+y=(3-y)²-5,x∈Q
5.Dupa o reducere cu10%,pretul unui sacou este de 270lei.Aflati pretul initial.
6.Elena cheltueste o suma de bani in trei zile asfel:in prima zi cheltueste doua treimi din suma si inca 15lei,a doua zi cheltueste 40%din rest,iar a treia zi cheltueste restul de27lei.Aflati:
a)ce suma a avut initial Elena.
b)Ce suma a cheltuit Elena in a doua zi.

Answer 1

1. a(c+d)+b(c+d)=(a+b)(c+d)=20x30=600
2.2/x=y/7 =>> xy=6 =>> (xy-7)^100=(-1)^100=1
3.a) 2a+2b+2c=90 =>> a+b+c=45 ; b) b=30-c ; c=40-a
b=30-40-a =>>b=-10-a
a-10-a+40-a=45 =>.-a=45+10-40 =>> a=15
5. 10/100 x 270 = 27.
270+27=297=pretul initial

Answer 2

4.Rezolvatii ecuatiile:
a)3x+1/√5=x+42/√20,x∈R
2x=42/√20-1/√5
2x=(42√5-√20)/√100
2x=(42√5-2√5)/10
2x=40√5/10
2x=4√5
x=2√5

b)(y+2)²+y=(3-y)²-5,x∈Q
y²+4y+4+y=9-6y+y²-5
+4y+4+y=9-6y-5
11y=0
y=0

5.
100%-10%=90%
270:90%=300 lei pretul initial

6 x=suma initiala
2x/3 + 15=1 zi
(x-2x/3 - 15) ×40%=(x/3 - 15) ×2/5=2x/15-6 = 1 2-a zi
2x/3+15+2x/15-6+27=x
15x-10x-2x=36×15
3x=540
x=180 lei
2x/15-6=2×180/15-6=24-6=18 lei a cheltuit a 2-a zi