62208 and M

Algebra Level 3

62208(a7+b7+c7+d7)2M(a2+b2+c2+d2)762208\big(a^{7}+b^{7}+c^{7}+d^{7}\big)^{2}\le M\big(a^{2}+b^{2}+c^{2}+d^{2}\big)^{7}

What is the smallest positive integer MM such that this inequality holds true for all a,b,c,da,b,c,d satisfying a,b,c,dRa,b,c,d\in \mathbb{R} and a+b+c+d=0?a+b+c+d=0?

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