Question

Rezolvati in R:
a) 4(la puterea x) + 12 = 14 * 2( la puterea x-1)
b) radical din x-2 = 6

Answer 1

a) (2²)^x + 12 = 14* 2^x * 2^(-1) (2²)^x + 12 = (14* 2^x )/ 2 (2²)^x + 12 = 7* 2^x Notam 2^x = t, t>0 => t²+12 = 7t t² - 7t + 12 = 0 Delta = 49-4*1*12 = 49-48 = 1 t1 = (7+1)/2 = 4 >0 t2 = (7-1)/2 = 3 >0 Ambele solutii convin; revenim la substitutie 2^x = 4 => x = 2 2^x = 3 (logaritmam) => x= log2 (3) b) √(x-2) = 6 C. E. : x-2>= 0 => x>=2 Ridicam la patrat x-2 = 36 x = 38 verifica conditia Daca ai vrut sa scrii doar x sub radical, rezolvarea este urmatoarea: √x = 6+2 C.E. : x>= 0 √x= 8 |*( )² x = 64 verifica conditia