Question

Cre este rezolvarea acestei ecuati : log2(x2-10)=3

Answer 1

conditia  de  existenta a  logaritmului
x²-10>0  x²>10=> x∈(-∞, -√10]U[√10 ,∞)=D
x²-10=2³=.> x²=18=>
x=+/-√18=+/-3√2∈domeniului  D  al  ecuatiei

Answer 2

㏒₂(x²-10)=3
CE:X²-10>0
x²-10=2³⇒
x²-10=8⇒x²-10-8=0⇒x²-18=0⇒
a=1
b=0
c=-18
Δ=b²-4ac⇒Δ=0²-4×1×(-18)⇒Δ=0+72⇒Δ=72⇒√Δ=√72⇒Δ=12√2
x1x2=-b+-√Δ/2a
x1=0+12√/2/2=12√2/2⇒6√2
x2=0-12√2/2=-12√2/2=-6/2
sucees