Решите неравенство а) 2x^2-13x+60 в)3x^2-6x+32>0. Created by NessyCampRock. algebra-ru

Решите неравенство а) 2x^2-13x+60 в)3x^2-6x+32>0...

NessyCampRock @NessyCampRock

July 2021 1 8 Report

Решите неравенство

а) 2x^2-13x+6<0
б)x^2-9>0

в)3x^2-6x+32>0

Answers & Comments

sangers1959

Verified answer

A)
2x²-13x+6<0
2x²-13x+6=0 D=121 √D=11
x₁=6 x₂=0,5 ⇒
2*(x-6)*(x-0,5)<0 |÷2
(x-6)*(x-0,5)<0
-∞_______+_______0,5_______-_______6_______+_______+∞
Ответ: x∈(0,5; 6).
б)
x²-9>0
x²-3²>0
(x+3)*(x-3)>0
-∞_____+_____-3_____-_____3_____+_____+∞
Ответ: x∈(-∞;-3)U(3;+∞).
в)
3x²-6x+32>0
3x²-6x+32=0
3x²-6x+3+29>0
3*(x²-2x+1)+29>0
3*(x-1)²+29>0 ⇒
Ответ: x∈(-∞;+∞).

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