Question

Suma rădăcinilor reale ale ecuației log5(x patrat+2x - 3) = 1 este​

Answer 1

log{a} ^b = c => b = a^c

x^2+2x-3= 5^1

x^2+2x-3-5=0

x^2+2x-7= 0

delta = 4+28 =32

x1=(-2+4V2)/2 = 2(-1+2V2)/2 = -1+2V2

x2=(-2-4V2)/2 = 2(-1-2V2)/2 = -1-2V2

suma x1+x2= -1+2V2+(-1-2V2) = -1+2V2-1-2V2= -2

Answer 2

$log_{5}( {x}^{2} + 2x - 3 ) = 1 \\ {x}^{2} + 2x - 3 = {5}^{1} \\ {x}^{2} + 2x - 3 = 5 \\ {x}^{2} + 2x - 3 - 5 = 0 \\ {x}^{2} + 2x - 8 = 0 \\ (x + 4) \times (x - 2) = 0 \\ x + 4 = 0 \\ x = - 4 \\ x - 2 = 0 \\ x = 2$

Suma rădăcinilor : -4+2=-2