Math, asked by dasyamshashekala965, 6 months ago

if a+ b + c = 9 and ab + bc + ca = 26 then find a2 + b2 +c2​

Answers

Answered by sikarwararchna8
1

Step-by-step explanation:

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

(9)^2 = a^2 + b^2 + c^2 + 2(ab + bc + ca)

81 = a^2 + b^2 + c^2 + 2(26)

81 - 52 = a^2 + b^2 + c^2

29 = a^2 + b^2 +c^2

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Answered by Anonymous
15

question:

if a+ b + c = 9 and ab + bc + ca = 26 then find a^2 + b^2 +c^2

solution:

29

Given:

if a+ b + c = 9 and ab + bc + ca = 26

To find:

find a^2 + b^2 +c^2

step by step explanation:

(i) on squaring both sides , we have:

  \implies\sf {a}^{2}  +  {b}^{2}  +  {c}^{2}  =  {9}^{2}

 \sf use \: identity - \boxed{  \sf {(a+ b+c)}^{2}  = {a}^{2} +  {b}^{2} + {c}^{2}  + 2ab + 2bc + 2ca}

 \implies \sf {a}^{2} +  {b}^{2} + {c}^{2} = 2(26) = 81

 \implies \sf {a}^{2} +  {b}^{2} + {c}^{2} = 52= 81

 \implies \sf {a}^{2} +  {b}^{2} + {c}^{2} = 81 - 52

 \implies \sf {a}^{2} +  {b}^{2} + {c}^{2} = 29

therefore:

\longrightarrow\underline{\underline{\red{\sf{{a}^{2} +  {b}^{2} + {c}^{2} = 29}}}}

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