Question

if 14(a²+b²+c²)=(a+2b+3c)² then a:b:c=?​

Answer 1

Answer:

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Step-by-step explanation:

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Answer 2

Answer:

1:2:3

Step-by-step explanation:

14(a^2+ b^2 +c^2) = (a+2b+3c)^2

⇒$14a^{2}+14b^{2}+14c^{2} = a^{2} + 4b^ 2 +9c^2+4ab+6ac+12bc$

⇒$13a^2+10b^2+5c^2-4ab-12bc-6ac=0$

⇒$(4a^2+b^2-4ab)+(9a^2+c^2-6ac)+(9b^2+4c^2-12bc)=0$

⇒$(2a-b)^2+(3a-c)^2-(3b-2c)^2=0$

Hence i get,

$2a-b=0\\3a-c=0\\3b-2c=0$

Solving the three equations i get a:b:c= 1:2:3