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

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=abab=1 a:b=1:1   b2=bcbc=1 b:c=1:1   c2=caca=1 c:a=1:1Therefore the required ratio is a:b:c=1:1:1

  • 10
What are you looking for?