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If a² + b² + c² - ab - bc - ca = 0 then a : b : c is?

11 : 2 : 1
22 : 1 : 1
31 : 1 : 2
41 : 1 : 1

Answer:- 1

Explanation:-

Solution:

\begin{aligned} Given, \\ a^{2} + b^{2} + c^{2} - a b - b c - c a = 0 \\ Find, a : b : c = ? \\ According to the question, \\ a^{2} + b^{2} + c^{2} - a b - b c - c a = 0 \\ \Rightarrow a^{2} + b^{2} + c^{2} = a b + b c + c a \\ Let a = b = c = 1 \\ \Rightarrow 1^{2} + 1^{2} + 1^{2} = 1 \times 1 + (1 \times 1) + (1 \times 1) \\ \Rightarrow 3 = 3 \\ \Rightarrow So, ratio of a : b : c = 1 : 1 : 1 \end{aligned}

$\eqalign{ & {\text{Given, }} \cr & {a^2} + {b^2} + {c^2} - ab - bc - ca = 0 \cr & {\text{Find, }}a:b:c = ? \cr & {\text{According to the question, }} \cr & {a^2} + {b^2} + {c^2} - ab - bc - ca = 0 \cr & \Rightarrow {a^2} + {b^2} + {c^2} = ab + bc + ca \cr & {\text{Let }}a = b = c = 1 \cr & \Rightarrow {1^2} + {1^2} + {1^2} = 1 \times 1 + \left( {1 \times 1} \right) + \left( {1 \times 1} \right) \cr & \Rightarrow 3 = 3 \cr & \Rightarrow {\text{So, ratio of }}a:b:c = 1:1:1 \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} Given, \\ a^{2} + b^{2} + c^{2} - a b - b c - c a = 0 \\ Find, a : b : c = ? \\ According to the question, \\ a^{2} + b^{2} + c^{2} - a b - b c - c a = 0 \\ \Rightarrow a^{2} + b^{2} + c^{2} = a b + b c + c a \\ Let a = b = c = 1 \\ \Rightarrow 1^{2} + 1^{2} + 1^{2} = 1 \times 1 + (1 \times 1) + (1 \times 1) \\ \Rightarrow 3 = 3 \\ \Rightarrow So, ratio of a : b : c = 1 : 1 : 1 \end{aligned}

$\eqalign{ & {\text{Given, }} \cr & {a^2} + {b^2} + {c^2} - ab - bc - ca = 0 \cr & {\text{Find, }}a:b:c = ? \cr & {\text{According to the question, }} \cr & {a^2} + {b^2} + {c^2} - ab - bc - ca = 0 \cr & \Rightarrow {a^2} + {b^2} + {c^2} = ab + bc + ca \cr & {\text{Let }}a = b = c = 1 \cr & \Rightarrow {1^2} + {1^2} + {1^2} = 1 \times 1 + \left( {1 \times 1} \right) + \left( {1 \times 1} \right) \cr & \Rightarrow 3 = 3 \cr & \Rightarrow {\text{So, ratio of }}a:b:c = 1:1:1 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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