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If the following expression results as: 5a 2 +9b 2 -12ab+4a+4=0. Find a 2 +b 2 -ab.

If the following expression results as:
5a2+9b2-12ab+4a+4=0. Find a2+b2-ab.

Grade:12th pass

1 Answers

nitish
36 Points
4 years ago
the given expression can be written as:
(4a^2+9b^2-12ab)+(a^2+4a+4)=0
this can be simplified as :
(3b-2a)^2+(a+2)^2=0
now ,as square terms i.e x^2 or anything,always gives you only positive values
therefore,this expression can go to zero only if both the terms separately go to zero.(i hope you undersatnd this)
(eg:x^2+y^2=0 only when x=0 or y=0)
therefore i ccan conclude that :
3b-2a=0 and a+2=0
hence a=-2 and 3b=-4 or b=-4/3
 
hence a^2+b^2-ab=(4)+(16/9)+(2)(4/3) = (36+16+24)/9
=76/9
 
 
 

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