a+b+c=12 and a^2+b^2+c^2=64
yoonie:
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Answered by
3
Answer : 80
Solution :
_________
Given that :
![a + b + c = 12 \: and \: {a }^{2} + {b}^{2} + {c}^{2} = 64 a + b + c = 12 \: and \: {a }^{2} + {b}^{2} + {c}^{2} = 64](https://tex.z-dn.net/?f=a+%2B+b+%2B+c+%3D+12+%5C%3A+and+%5C%3A++%7Ba+%7D%5E%7B2%7D++%2B++%7Bb%7D%5E%7B2%7D++%2B++%7Bc%7D%5E%7B2%7D++%3D+64+)
As we know that :
![{(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ \\ = > {(12)}^{2} = 64 + 2(ab + bc + ca) \\ \\ = > 2(ab + bc + ca) = 144 - 64 = 80 {(a + b + c)}^{2} = {a}^{2} + {b}^{2} + {c}^{2} + 2(ab + bc + ca) \\ \\ = > {(12)}^{2} = 64 + 2(ab + bc + ca) \\ \\ = > 2(ab + bc + ca) = 144 - 64 = 80](https://tex.z-dn.net/?f=+%7B%28a+%2B+b+%2B+c%29%7D%5E%7B2%7D++%3D++%7Ba%7D%5E%7B2%7D++%2B++%7Bb%7D%5E%7B2%7D++%2B++%7Bc%7D%5E%7B2%7D++%2B+2%28ab+%2B+bc+%2B+ca%29+%5C%5C++%5C%5C++%3D++%26gt%3B++%7B%2812%29%7D%5E%7B2%7D++%3D+64+%2B+2%28ab+%2B+bc+%2B+ca%29++%5C%5C++%5C%5C++%3D++%26gt%3B+2%28ab+%2B+bc+%2B+ca%29+%3D+144+-+64+%3D+80)
So, the answer will be 80
Solution :
_________
Given that :
As we know that :
So, the answer will be 80
Answered by
0
What's ur question ???....
The question is incomplete....
Though, I think u wanna ask the value of
(ab + bc + ca).....
(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab +bc +ca)
So,
12^2 = 64 + 2(ab + bc + ca)
Hence,
ab + bc +ca is 40
The question is incomplete....
Though, I think u wanna ask the value of
(ab + bc + ca).....
(a + b + c)^2 = a^2 + b^2 + c^2 + 2(ab +bc +ca)
So,
12^2 = 64 + 2(ab + bc + ca)
Hence,
ab + bc +ca is 40
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