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UnDeadMoroz
@UnDeadMoroz
October 2021
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[tex] 9^{x}-7*3^{x}-18\ \textless \ 0[/tex] решите показательное неравенство
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sangers1959
Verified answer
9ˣ-7*3ˣ-18<0
3²ˣ-7*3ˣ-18<0
Пусть t=3ˣ>0 ⇒
t²-7x-18<0 D=121
t₁=9 t₂=-2
(t-9)(t+2)<0
(3ˣ-9)(3ˣ+2)<0
Так как 3ˣ+2>0 ⇒
3ˣ-9<0
3ˣ<9
3ˣ<3² ⇒
x<2.
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Answers & Comments
Verified answer
9ˣ-7*3ˣ-18<03²ˣ-7*3ˣ-18<0
Пусть t=3ˣ>0 ⇒
t²-7x-18<0 D=121
t₁=9 t₂=-2
(t-9)(t+2)<0
(3ˣ-9)(3ˣ+2)<0
Так как 3ˣ+2>0 ⇒
3ˣ-9<0
3ˣ<9
3ˣ<3² ⇒
x<2.