Question

if a2+b2+c2=32 and ab+bc+ca=25 then a+b+c=?​

Answer 1

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• a² + b² + c² = 32 and ab + bc + ca = 25 then value of a + b + c = ?

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Here is identity to solve this question !

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$\boxed{ \bold \pink{{(a + b+ c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca)}}$

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Let's find our answer .-.

$\bold \orange{{ \leadsto \: (a + b+ c)}^{2} = 32+ 2(25)}$

$\bold \green{{ \leadsto \: (a + b+ c)}^{2} = 32+ 50}$

$\bold \orange{{ \leadsto \: (a + b+ c)}^{2} = 82}$

$\boxed{ \bold \red{ (a + b+ c) = \sqrt{82} }}$

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$\boxed{ \fcolorbox{cyan}{black}{ \boxed{\bold \pink{ \boxed{ \fcolorbox{cyan}{orange}{ \boxed{\bold \purple{ Answer \implies \: (a+b+c) = \sqrt{82} }}}}}}}}$

Answer 2

(a+b+c)

2

=a

2

+b

2

+c

2

+2(ab+bc+ca)

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Let's find our answer .-.

\bold \orange{{ \leadsto \: (a + b+ c)}^{2} = 32+ 2(25)}⇝(a+b+c)

2

=32+2(25)

\bold \green{{ \leadsto \: (a + b+ c)}^{2} = 32+ 50}⇝(a+b+c)

2

=32+50

\bold \orange{{ \leadsto \: (a + b+ c)}^{2} = 82}⇝(a+b+c)

2

=82

\boxed{ \bold \red{ (a + b+ c) = \sqrt{82} }}

(a+b+c)=

82

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