√ ( x - 2 ) = x - 4
( √ ( x - 2 ))² = ( x - 4 )²
x - 2 ≥ 0 ; x ≥ 2
x - 4 ≥ 0 ; x ≥ 4
ОДЗ [4 ; + ∞ )
x - 2 = x² - 8x + 16
x² - 9x + 18 = 0
D = 81 - 72 = 9 = 3²
x1 = ( 9 + 3 ) : 2 = 6
x2 = ( 9 - 3 ) : 2 = 3 ( не подходит )
Ответ 6
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{log(2,1)(x²+2x-10≥log(2,1)(x+2)
{|x|<7
1)
{x+2>0⇒x>-2
{x²+2x-10>0 D=4+40=42 x1<(-2-√42)/2 U x2>(-2+√42)/2
{x²+2x-10≥x+2⇒x²+x-12≥0 x1+x2=-1 U x1*x2=-12 x1≤-4 U x2≥3
x≥3
2)
-7<x<7
x∈[3;7)
x²-4x+5 = x²-4x+4+1 = (х-2)²+1.