If a^4+b^4+c^4+d^4=4abcd. Prove that a=b=c=d
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a⁴, b⁴ , c⁴ and d⁴ all are positive so,
AM≥ GM
(a⁴ + b⁴ + c⁴ + d⁴)/4 ≥ ( a⁴b⁴c⁴d⁴)¼
a⁴ + b⁴ + c⁴ + d⁴ ≥ 4abcd
but here ,
a⁴ + b⁴ + c⁴ + d⁴ = 4abcd
this is possible only when,
a = b = c = d
AM≥ GM
(a⁴ + b⁴ + c⁴ + d⁴)/4 ≥ ( a⁴b⁴c⁴d⁴)¼
a⁴ + b⁴ + c⁴ + d⁴ ≥ 4abcd
but here ,
a⁴ + b⁴ + c⁴ + d⁴ = 4abcd
this is possible only when,
a = b = c = d
Answered by
0
Answer:
a⁴, b⁴ , c⁴ and d⁴ all are positive so,
AM≥ GM
(a⁴ + b⁴ + c⁴ + d⁴)/4 ≥ ( a⁴b⁴c⁴d⁴)¼
a⁴ + b⁴ + c⁴ + d⁴ ≥ 4abcd
but here ,
a⁴ + b⁴ + c⁴ + d⁴ = 4abcd
this is possible only when,
a = b = c = d
Step-by-step explanation:
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