Question

1.Daca 6 supra a =3 supra 2 ,atunci numarul a este egal cu...
2. Se cosidera relatia a + 1 supra a =3 , a € R *.Sa se calculeze a la a doua +1 supra a la a doua

Answer 1

1) 6÷a=3÷2
a=6×2÷3
a=12÷3
a=4
2) (a+1)÷a=3
a+1=3×a
3×a-a=1
2×a=1
a=1÷2
(a^2+1)÷a^2=
=((1÷2)^2+1)÷(1÷2)^2
=(1÷4+1)÷1÷4
=(1÷4+4÷4)÷1÷4
=5÷4:1÷4
=5÷4×4÷1
=5

Answer 2

$1)\;\;\frac{6}{a}=\frac{3}{2}\;\;\Rightarrow\;\;a=\frac{2\cdot6}{3}=4\;;$

$2)\;\;a+\frac{1}{a}=3\;\\ \Rightarrow\;\; (a+\frac{1}{a})^2=3^2\\ .\;\;\;\;\;\;a^2+2\cdot{a}\cdot\frac{1}{a}+\frac{1}{a^2}=9\\ deci:\;\;\;a^2+\frac{1}{a^2}=9-2=7$