помогите 25 балов, алгебра . Created by egorpyrlifyn. algebra-ru

помогите 25 балов, алгебра ...

egorpyrlifyn @egorpyrlifyn

July 2022 1 11 Report

помогите 25 балов, алгебра

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axatar

Verified answer

Ответ:

1) a>b

2) Доказательство в части объяснения.

Объяснение:

1) $b+3=a+2\sqrt{2}\\b-a=2\sqrt{2}-3\\(b-a)^{2}=(2\sqrt{2}-3)^{2}\\(b-a)^{2}=4*2-2*3*2\sqrt{2}+9=17-6\sqrt{2}>17-6*2>17-12>5\\(b-a)^{2}>5\\b-a>\sqrt{5}>0\\ b>a$

2) $\frac{a^{2}+9b^{2}}{6}-ab=\frac{a^{2}+9b^{2}-6ab}{6}=\frac{a^{2}-2*a*3*b+(3b)^{2}}{6}=\\=\frac{(a-3b)^{2}}{6}\geq 0$ ⇒

⇒ $\frac{a^{2}+9b^{2}}{6}-ab\geq 0$ ⇒ $\frac{a^{2}+9b^{2}}{6}\geq ab$

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