<s>[INST] $c$ is the value of $x^3+3x-14$ where $x=\sqrt[3]{7+5\sqrt2}-\frac{1}{\sqrt[3]{7+5\sqrt2}}$.Find the value of $a+b+c$ $a=\sqrt{57+40\sqrt2}-\sqrt{57-40\sqrt2}$ and $b=\sqrt{25^{\frac{1}{\log_85}}+49^{\frac{1}{\log_67}}}$ and $c$ is the value of $x^3+3x-14$ where $x=\sqrt[3]{7+5\sqrt2}-\frac{1}{\sqrt[3]{7+5\sqrt2}}$.Find the value of $a+b+c$.

I tried to solve and simplify this problem but no luck.Please help me.Thanks.
 [/INST] (1) $a=(5+4\sqrt{2})-(4\sqrt{2}-5)=10$
(2) $b=\sqrt{25^{\log_5{8}}+49^{\log_7{6}}}=\sqrt{8^2+6^2}=10$
(3) $x=\sqrt[3]{7+5\sqrt2}-\frac{1}{\sqrt[3]{7+5\sqrt2}}=(\sqrt{2}+1)-\frac{1}{\sqrt{2}+1}=(\sqrt{2}+1)-(\sqrt{2}-1)=2$, $c=8+6-14=0$
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