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m672
@m672
December 2021
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Найти наименьшее значение выражения
(3x+2y)^2 + 5(3x+2y)+18
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Verified answer
(3x+2y)^2 + 5(3x+2y)+18 =
{(3x+2y)^2 + 2*(3x+2y)*2,5+2,5^2}+18-2,5^2 =
={(3x+2y+2,5)^2}+18-2,5^2
3x+2y+2,5=t
(3x+2y)^2 + 5(3x+2y)+18 = t^2+18-6,25=
t^2+
11,75
ответ 11,75
2 votes
Thanks 2
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Answers & Comments
Verified answer
(3x+2y)^2 + 5(3x+2y)+18 = {(3x+2y)^2 + 2*(3x+2y)*2,5+2,5^2}+18-2,5^2 =={(3x+2y+2,5)^2}+18-2,5^2
3x+2y+2,5=t
(3x+2y)^2 + 5(3x+2y)+18 = t^2+18-6,25=t^2+11,75
ответ 11,75