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Question Number 170064 by mathlove last updated on 15/May/22

(((a−2))/2)=(((b−3))/3)=(((c−4))/4) and a∙b∙c=192 faind a+b+c=?

(a−2)2=(b−3)3=(c−4)4anda⋅b⋅c=192fainda+b+c=?

Answered by Rasheed.Sindhi last updated on 15/May/22

(((a−2))/2)=(((b−3))/3)=(((c−4))/4) and a∙b∙c=192 find a+b+c=? ((a−2)/2)+1=((b−3)/3)+1=((c−4)/4)+1 (a/2)=(b/3)=(c/4)=((a+b+c)/(2+3+4))=k(say) (a/2)=(b/3)=(c/4)=((a+b+c)/9)=k(say) a=2k, b=3k, c=4k, a+b+c=9k a∙b∙c=2k.3k.4k=192 24k^3 =192 k^3 =8⇒k=2 a+b+c=9k=9(2)=18

(a−2)2=(b−3)3=(c−4)4anda⋅b⋅c=192finda+b+c=?a−22+1=b−33+1=c−44+1a2=b3=c4=a+b+c2+3+4=k(say)a2=b3=c4=a+b+c9=k(say)a=2k,b=3k,c=4k,a+b+c=9ka⋅b⋅c=2k.3k.4k=19224k3=192k3=8⇒k=2a+b+c=9k=9(2)=18

Answered by som(math1967) last updated on 15/May/22

let ((a−2)/2)=((b−3)/3)=((c−4)/4)=k ⇒a=2(k+1) ,b=3(k+1),c=4(k+1) 2×3×4×(k+1)^3 =abc ⇒(k+1)^3 =((192)/(24))=8 ⇒k+1=2⇒k=1 a+b+c=2(k+1)+3(k+1)+4(k+1) =4+6+8=18 ans

leta−22=b−33=c−44=k⇒a=2(k+1),b=3(k+1),c=4(k+1)2×3×4×(k+1)3=abc⇒(k+1)3=19224=8⇒k+1=2⇒k=1a+b+c=2(k+1)+3(k+1)+4(k+1)=4+6+8=18ans

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