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sửa đổi
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.·’*★Used.·’★to.·’*★.·’*
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.·’*★Used.·’★to.·’*★.·’* For all nonnegative real numbers $a,b$ and $c.$ Prove that: $\color{blue}{\sum_{cyc}a^2\sum_{cyc}a(b+c)\sum_{cyc}\frac{1}{(b+c)^2}\geq (a+b+c)^4}$
.·’*★Used.·’★to.·’*★.·’* For all nonnegative real numbers $a,b$ and $c.$ Prove that: $\color{blue}{\sum_{cyc}a^2\sum_{cyc}a(b+c)\sum_{cyc}\frac{1}{(b+c)^2}\geq (a+b+c)^4}$ Solution: $\sum_{cyc}\frac{1}{(a+b)^2}\geq \frac{3(a+b+c)^2}{8(ab+bc+ca)}(\frac{1}{ab+bc+ca}+\frac{1}{a^2+b^2+c^2})$
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sửa đổi
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.·’*★Used.·’★to.·’*★.·’*
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Prove t hat: $\co lor{blue}{\sum_{cyc}a^2\sum_{cyc}a(b+c)\sum_{cyc}\frac{1}{(b+c)^2}\geq (a+b+c)^4}$For all nonnegative real numbers $a,b$ and $c.$ Prove that: $\color{ blue}{\sum_{cyc}a^2\sum_{cyc}a(b+c)\sum_{cyc}\frac{1}{(b+c)^2}\geq (a+b+c)^4}$
.·’*★Use d.·’★to .·’*★.·’*For all nonnegative real numbers $a,b$ and $c.$ Prove that: $\color{ pink}{\sum_{cyc}a^2\sum_{cyc}a(b+c)\sum_{cyc}\frac{1}{(b+c)^2}\geq (a+b+c)^4}$
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sửa đổi
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¸.·’*★Unnamed★secret.·’*★*¸.·’
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Prove that: $\frac {1}{(a+b)^2}+\fr ac{1}{(b+c)^2}+\frac{1}{(c+a)^2}\ge q \frac{3\sqrt {3abc(a+b+c)}(a+b+c)^2}{4(ab+bc+ca)^3}$For all nonnegative real numbers $a,b$ and $c,$ no two of which aer zero$.$Prove that: $\frac{1}{(a+b)^2}+\frac{1}{(b+c)^2}+\frac{1}{(c+a)^2}\geq \frac{3\sqrt{3abc(a+b+c)}(a+b+c)^2}{4(ab+bc+ca)^3}$
¸.·’*★Unna med★secret .·’*★*¸.·’For all nonnegative real numbers $a,b$ and $c,$ no two of which aer zero$.$Prove that: $\frac{1}{(a+b)^2}+\frac{1}{(b+c)^2}+\frac{1}{(c+a)^2}\geq \frac{3\sqrt{3abc(a+b+c)}(a+b+c)^2}{4(ab+bc+ca)^3}$
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