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If a, b, c be positive real numbers then prove that

Namrata Saha , 4 Years ago
Grade 12th pass
anser 1 Answers
Srutarshi Tripathi

Last Activity: 4 Years ago

Required to Prove :
(a2b + b2c + c2a)(ab2 +  bc2 + ca2) > 9a2b2c2
or, abc(a/c + b/a + c/b ) x abc(b/c + c/a + a/b) > 9a2b2c2
or, (a/c + b/a + c/b )2 > 9
Proof:
applying AM-GM INEQUALITY,
a/c + b/a + c/b > 3
Hence , squaring both sides we get the required inequality
 

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