a+b+c=4root3 and a2+b2+c2=16 then the ratio a:b:c is - Maths - Mathematical Reasoning

Question

a+b+c=4root3 and a2+b2+c2=16 then the ratio a:b:c is

Vijay Kumar Gupta · Accepted Answer

Its is given that,    a+b+c=43  and a2+b2+c2=16Use teh algebraic formula     a+b+c2=a2+b2+c2+2ab+2bc+2caSubstitute the values to get,     432=16+2ab+bc+ca              48=16+2ab+bc+caThis implies that,      2ab+bc+ca=48-16      2ab+bc+ca=32             ab+bc+ca=16Compare a2+b2+c2=16 and ab+bc+ca=16   a2=ab⇒ab=1 ⇒a:b=1:1   b2=bc⇒bc=1 ⇒b:c=1:1   c2=ca⇒ca=1 ⇒c:a=1:1Therefore the required ratio is a:b:c=1:1:1