exercițiile 2, 5 și 6 :))

[tex]2\cdot \:3^x+3^{x+1}=45 \\ 2\cdot \:3^x+3^{x+1} \\ =2\cdot \:3^x+3^1\cdot \:3^x \\ =3^x\left(2+3^1\right) \\ =5\cdot \:3^x \\ 5\cdot \:3^x=45 \\ \frac{5\cdot \:3^x}{5}=\frac{45}{5} \\ 3^x=9 \\ 3^x=3^2 \\ x=2 \\ \\ [/tex]

2) 2 * 3ˣ + 3ˣ⁺¹ = 45
    2 * 3ˣ + 3ˣ * 3 = 45
   5 * 3ˣ = 45
   3ˣ = 9
   3ˣ = 3²
   x=2

[tex]MNPQ~paralelogram~\ \textless \ =\ \textgreater \ \left \{ {{x_{M}+ x_{Q}= x_{N} + x_{P} } \atop {y_{M} +y _{Q} =y_{N} +y_{P} }} \right. \\ \\ \left \{ {{ x_{Q} = x _{N} + x_{P} - x_{M} } \atop {y_{Q} = y_{N} + y_{P} - y_{M} }} \right. \\ \\ \left \{ {{ x_{Q}=5+7-1 } \atop { y_{Q}=5+11-1 }} \right. \\ \\ \left \{ {{ x_{Q}=11 } \atop { y_{Q}=15 }} \right. \\ \\ Q(11,15)[/tex]

6) sin(90°-x) * cos x + cos(90°-x) * sin x = 1, ∀, x∈(0°, 90°)
    sin (90°-x) * cos x + cos(90°-x) * sin x = 1
    cos x * cos x + sin x * sin x = 1
    cos²x + sin²x = 1
    1=1 (adevarat)