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netesovakatya
@netesovakatya
July 2022
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(x^1/2)-(7x^1/4)+6<0
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oganesbagoyan
Verified answer
√x - 7*x^(1/4) +6 <0 ; ОДЗ:
x
≥ 0.
замена переменной t =x^(1/4) ⇒t²=(x^(1/4))² =√x.
t² -7t +6 <0 ;
t² -(1+6)t +1*6 =0 ⇒t₁ =1, t₂ =6.
(t -1)(t-6) <0 ;
по методу интервалов :
+ - +
---- 1------ 6 ------
1< t <6 ;
1<
x^(1/4) <6 ;
1< x < 6
⁴.
ответ : x∈(1 ;12296)
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Answers & Comments
Verified answer
√x - 7*x^(1/4) +6 <0 ; ОДЗ: x ≥ 0.замена переменной t =x^(1/4) ⇒t²=(x^(1/4))² =√x.
t² -7t +6 <0 ;
t² -(1+6)t +1*6 =0 ⇒t₁ =1, t₂ =6.
(t -1)(t-6) <0 ;
по методу интервалов :
+ - +
---- 1------ 6 ------
1< t <6 ;
1<x^(1/4) <6 ;
1< x < 6⁴.
ответ : x∈(1 ;12296)