If a ^2 + b ^2 + c ^2 = 30 and a + b + c = 10, then find the value of ab + bc + ca.
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Answered by
33
squaring a + b + c = 10
[ (a + b) + c ]2 = 10 *10
(a+b)2 + 2 (a + b)*c + c2 = 100
a2 + 2ab + b2 + 2ac + 2bc + c2 = 100
a2 + 2 (ab + ac + bc ) + b2 + c2 = 100
a2 + 2 (ab + ac + bc ) + b2 + c2 = 100
(a2 + b2 + c2) + 2 (ab + ac + bc) = 100
30 + 2 ( ab + ac + bc) = 100
2(ab + ac + bc) + 30= 100
(ab + ac + bc) = (100 -30)/2
(ab + ac + bc) = 35
[ (a + b) + c ]2 = 10 *10
(a+b)2 + 2 (a + b)*c + c2 = 100
a2 + 2ab + b2 + 2ac + 2bc + c2 = 100
a2 + 2 (ab + ac + bc ) + b2 + c2 = 100
a2 + 2 (ab + ac + bc ) + b2 + c2 = 100
(a2 + b2 + c2) + 2 (ab + ac + bc) = 100
30 + 2 ( ab + ac + bc) = 100
2(ab + ac + bc) + 30= 100
(ab + ac + bc) = (100 -30)/2
(ab + ac + bc) = 35
Answered by
5
Answer:
Step-by-step explanation:
squaring a + b + c = 10
[ (a + b) + c ]2 = 10 *10
(a+b)2 + 2 (a + b)*c + c2 = 100
a2 + 2ab + b2 + 2ac + 2bc + c2 = 100
a2 + 2 (ab + ac + bc ) + b2 + c2 = 100
a2 + 2 (ab + ac + bc ) + b2 + c2 = 100
(a2 + b2 + c2) + 2 (ab + ac + bc) = 100
30 + 2 ( ab + ac + bc) = 100
2(ab + ac + bc) + 30= 100
(ab + ac + bc) = (100 -30)/2
(ab + ac + bc) = 35
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