Question

HELP PLSS ! URGENT!
1)Calculati media aritmetica si cea geometrica a numerelor x=√2 - 1 si y=√2 + 1
2)Rezolvati in multimea numerelor rationale ecuatia 4x-1 supra 5 - 3x-12 supra 10 = 2x+3 supra 6
3) stabiliti daca numarul n=(2√3 - √2)²-(√6-2)² este natural
4)Calculati (5x+1)²-2(5x+1)(5x-1)-(5x-1)2=
5)Se dau triunghiurile asemenea ABC si DEF . Daca AB=6cm , BC=7 cm , AC=9cm si DE=18 cm , sa se afle lungimile laturilor EF si DF
6) Calculati : 2supra5 * 10supra7 * 14supra9 * 18supra10 * 20supra11 * 22supra15 : (0,(1) + 0,(7))=

Answer 1

1)Calculati media aritmetica si cea geometrica a numerelor x=√2 - 1 si y=√2 + 1
ma=[(√2 - 1 )+(√2 + 1 )]/2=2√2/2=√2

mg=√(√2 - 1 )(√2 + 1 )=√(2-1)=√1=1
2)Rezolvati in multimea numerelor rationale ecuatia 4x-1 supra 5 - 3x-12 supra 10 = 2x+3 supra 6
(4x-1)/5 - (3x-12)/10 = (2x+3)/6
24x-6-9x+36=10x+15
5x=15-36+6
5x=-15
x=-3

3) stabiliti daca numarul n=(2√3 - √2)²-(√6-2)² este natural
n=(2√3 - √2)²-(√6-2)² =
=12 + 2-4√6-6-4+4√6 =
=12 + 2-6-4 =
=14-10=
=4

 4)Calculati (5x+1)²-2(5x+1)(5x-1)-(5x-1)2=

(5x+1)²-2(5x+1)(5x-1)-(5x-1)²=
=[(5x+1)-(5x-1)]²=
=(5x+1-5x+1)²=
=2²=4

5)Se dau triunghiurile asemenea ABC si DEF . Daca AB=6cm , BC=7 cm , AC=9cm si DE=18 cm , sa se afle lungimile laturilor EF si DF
AB/DE=BC/EF=AC/DF
6/18=7/EF=9/DF
1/3=7/EF=9/DF
EF=7*3=21 cm
DF=9*3=27cm

6) Calculati : 2supra5 * 10supra7 * 14supra9 * 18supra10 * 20supra11 * 22supra15 : (0,(1) + 0,(7))=

2/5 * 10/7 * 14/9 * 18/10 * 20/11 * 22/15 : (0,(1) + 0,(7))=
=64/15 : (1/9 + 7/9)=
=64/15 : 8/9=
=64/15 ×9/8=
=8*3/5=24/5=4,8