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Question Number 148428 by 0731619 last updated on 27/Jul/21

Answered by Mathspace last updated on 27/Jul/21

(((a+b)^2 )/(ab))−3 =(((a+b)^2 −3ab)/(ab)) =((a^2 +2ab+b^2 −3ab)/(ab)) =((a^2 −ab+b^2 )/(ab))=((a^2 −2a(b/2)+(b^2 /4)+b^2 −(b^2 /4))/(ab)) =(((a−(b/(2 )))^2 +((3b^2 )/4))/(ab))>0

(a+b)2ab−3=(a+b)2−3abab=a2+2ab+b2−3abab=a2−ab+b2ab=a2−2ab2+b24+b2−b24ab=(a−b2)2+3b24ab>0

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