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Prove that 1/(a-b)² +1(b-c)²+1/(c-a)² is a perfect square. |
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Answer» Answer: Answer Given, a 2 +b 2 +C 2 −ab−bc−ca multiply and divide by 2 = 2 2
×(a 2 +b 2 +c 2 −ab−bc−ca) = 2 a 2 −2ab+b 2 +b 2 −2bc+c 2 +c 2 −2ac+a 2
= 2 (a−b) 2 +(b−c) 2 +(c−a) 2
square of a number is always GREATER than or equal to zero. ∴(a−b) 2 +(b−c) 2 +(c−a) 2 ≥0 and (a−b) 2 +(b−c) 2 +(c−a) 2 =0 when a=b=c Hence, a 2 +b 2 +c 2 −ab−bc−ca is always non negative |
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