Math, asked by atulyaraj100, 1 year ago

Help me its very urgent i want the solution

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Answers

Answered by HimanshuR
1

a + b + c = 9 \\squaring \: both \: sides \\  (a + b + c) {}^{2} = (9 ){}^{2}  \\ a {}^{2}   +  {b}^{2}  +  {c}^{2}  + 2(ab + bc + ca) = 81 \\
it \: is \: given \: that \: a {}^{2}  +  {b}^{2}  +  {c}^{2}  = 35
So,
35 + 2( ab+  bc+  ca) = 81 \\ 2(ab +  bc+ ca) = 81 - 35 \\ ab + bc + a =  \frac{46}{2}  \\ ab +bc  +c a = 23
Now,
We know that
a {}^{3}  +  {b}^{3}   + {c}^{3}  - 3abc \\  = ( a+ b + c)(a {}^{2}  +  {b}^{2}  +  {c}^{2}  - ab - bc - ca) \\   = (a + b + c)( {a}^{2}  +  {b}^{2}  +  {c}^{2}  - (ab + bc + ca) \: ) \\
It is given that ,
a + b + c = 9(given) \\ a {}^{2}  +  {b}^{2 } +  {c}^{2}  = 35 (given)\\ ab + bc + ca = 23 (calculated \: above)
So,
 = (9) \times (35 - (23) \: ) \\  = 9 \times 12 \\  = 108
so \\  {a}^{3}  +  {b}^{3}  +  {c}^{3}  - 3abc = 108


----------Hope this will help you-----------
Answered by AlwaysSmile
1
Hey friend ,

Here is your answer ,
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a + b + c = 9
a² + b² + c² = 35

(a+b+c)² = a²+b²+c²+2(ab+bc+ca)

81 = 35 + 2(ab+bc+ca)
46 = 2(ab+bc+ca)
23 = ab+bc+ca

a³+b³+c³ - 3abc = (a+b+c)(a²+b²+c² - (ab+bc+ca))

a³+b³+c³ - 3abc
= 9(35-23)
= 9*12
= 108                         
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Hope it helped you !!
Please mark as brainliest !!
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