Question

Sa se rezolve in multimea nr. reale ecuatia
1)5 la x²=5
2)log₂ (1-√x+1)= -1

Answer 1

1)
$5^{ x^{2} } = 5^{1}$

=> x² = 1
=> x = ± 1
x₁ = 1
x₂ = -1

2)
[tex] log_{2} (1 - \sqrt{x+1} ) = -1 [/tex]

=> 1 - √(x + 1) = 2⁻¹
1 - √(x + 1) = 1 / 2
- √(x + 1) = 1/2 - 1
-√(x + 1) = -1/2    l  * (-1)
√(x + 1) = 1 / 2
x + 1 = ± 1 / 4
Ridicarea la putere poate sa introduca solutii false
a)
x + 1 = 1/4
x = 1/4 - 1 = -3/4

b)
x + 1 = -1/4
x = -1/4 - 1 = -5/4