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Question Number 194325 by horsebrand11 last updated on 03/Jul/23
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Answered by AST last updated on 04/Jul/23
(((x^4 +y^4 +z^4 )/3))^(1/4_ ) ≥(√((x^2 +y^2 +z^2 )/3))=(√(5/3))⇒Σx^4 ≥((25)/3)  Σx^4 =(Σx^2 )^2 −2Σx^2 y^2 =25−2Σx^2 y^2   ⇒Σx^4 ≤25−0(since Σx^2 y^2 ≥0 and max occurs at 0)
x4+y4+z434x2+y2+z23=53Σx4253Σx4=(Σx2)22Σx2y2=252Σx2y2Σx4250(sinceΣx2y20andmaxoccursat0)

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