From the given information in the question, what is the value of #(a+b+c)^2# ?

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Answer 1 · 2017-10-14T06:15:16

option (3)

So sum of roots #=(k+1)/k+(k+2)/(k+1)=-b/a.....[1]#

and product of roots #=(k+1)/kxx(k+2)/(k+1)=c/a#

#=>(k+2)/k =c/a....[2]#

From [2] we get

#1+2/k=c/a#

#=>2/k=c/a-1=(c-a)/a#

#=>k=(2a)/(c-a).....[3]#

Subtracting {1]from [2] we get

#(b+c)/a=(k+2)/k -(k+1)/k-(k+2)/(k+1)#

#=>(b+c)/a=1+2/k -1-1/k-1-1/(k+1)#

#=>(b+c)/a+1=1/k-1/(k+1)#

#=>(b+c+a)/a=1/(k(k+1))#

#=>(b+c+a)/a=1/((2a)/(c-a)((2a)/(c-a)+1))#

#=>(b+c+a)/a=(c-a)^2/(2a(c+a))#

#=>2(b+c+a)(c+a)=(c-a)^2#

#=>2b(c+a)+2(c+a)^2-(c-a)^2=0#

#=>2bc+2ab+(c+a)^2 +4ac=0#

#=>a^2+b^2+c^2+2bc+2ab+2ca =b^2-4ac#

#=>(a+b+c)^2=b^2-4ac#