Question

решите неравенство
(х²-2х+1)(х²-2х+3)<3
( С объяснением!)​

Answer 1

$\displaystyl\bf\\(x^{2} -2x+1)(x^{2} -2x+3)<3\\\\x^{2} -2x+1=m \ \ ; \ \ \ \Rightarrow \ \ x^{2} -2x+3=m+2\\\\m(m+2)<3\\\\m^{2} +2m-3<0\\\\(m+3)(m-1)<0$

+ + + + + (- 3) - - - - - (1) + + + + +   m

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$\displaystyle\bf\\m\in(-3 \ ; \ 1)\\\\1) \ m>-3\\\\x^{2} -2x+1>-3\\\\x^{2} -2x+4>0\\\\x^{2} -2x+4=0\\\\D=(-2)^{2} -4\cdot4=4-16=-12<0\\\\x\in R\\\\2)\\\\x^{2}-2x+1<1\\\\x^{2} -2x<0\\\\x(x-2)<0$

+ + + + + (0) - - - - - (2) + + + + +

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$\displaystyle\bf\\Otvet:x\in(0 \ ; \ 2)$