Question

If (a+b+c)²= 3(ab+bc+ca) then prove that. a²\bc+ b²/ca+c²/ab=3​

Answer 1

Step-by-step explanation:

a^3+b^3+c^3 -3abc = (a^2+b^2+c^2-ab-bc-ca)(abc) ----(1)

according to question :-

(a+b+c)^2 = 3(ab+bc+ca)

a^2 + b^2+ c^2 + 2(ab + bc + ca) = 3(ab + bc + ca)

a^2 + b^2 + c^2 = 3(ab + bc + ca) - 2(ab + bc + ca)

a^2 + b^2 + c^2 = ab + bc + ca--- (2)

substitute (2) in (1)

a^3+b^3+c^3 - 3abc = (ab+bc+ca-ab-bc-ca)(abc)

a^3+b^3+c^3 = 3abc

divide both sides with abc

(a^3+b^3+c^3)/abc = 3abc / abc

a^3/abc + b^3/abc + c^3/abc = 3

a^2/bc + b^2/ac + c^2/ab = 3

hope this helps please mark as brainliest