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Anastasia29ru
@Anastasia29ru
July 2022
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Помогите!!! Найдите число целых решений неравенства: x2+x<72
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ShirokovP
Verified answer
X^2 + x < 72
x^2 +x - 72< 0
D = 1 + 4*72 = 1 + 288 = 289 = 17^2
x1 = ( - 1 + 17)/2 = 16/2 = 8 ;
x2 = ( - 1 - 17)/2 = - 18/2 = - 9;
(x + 9) ( x - 8) < 0
+ - +
------------- ( - 9) ------------- ( 8 ) ------------> x
x ∈ ( - 9; 8)
Целые решения:
- 8 ; - 7; - 6; - 5; - 4;
-
3; - 2; - 1; 0 ; 1
;
2 ; 3; 4 ; 5 ; 6
; 7
Ответ: 16
3 votes
Thanks 1
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Answers & Comments
Verified answer
X^2 + x < 72x^2 +x - 72< 0
D = 1 + 4*72 = 1 + 288 = 289 = 17^2
x1 = ( - 1 + 17)/2 = 16/2 = 8 ;
x2 = ( - 1 - 17)/2 = - 18/2 = - 9;
(x + 9) ( x - 8) < 0
+ - +
------------- ( - 9) ------------- ( 8 ) ------------> x
x ∈ ( - 9; 8)
Целые решения:
- 8 ; - 7; - 6; - 5; - 4; - 3; - 2; - 1; 0 ; 1 ; 2 ; 3; 4 ; 5 ; 6 ; 7
Ответ: 16