Question

$logsqrt{2}( x^{2} -3x)=4$ помогите плизз

Answer 1

log2^1/2(x²-3x)=4         ОДЗ   x²-3x>0⇒x(x-3)>0

2log2(x²-3x)=log2(16)                ____+__0 ___-____3 _+_

log2(x²-3x)²=log2(16)

(x²-3x)²=16

(x²-3x)²-4²=0

(x²-3x-4)(x²-3x+4)=0

x²-3x-4=0                  x²-3x+4=0

D=9+16=25              D=9-16=-7 -корней нет

x1=(3+5)/2=4

x2=(3-5)/2=-1