Question
Download Solution PDFIf a + b + c = 10 and a2 + b2 + c2 = 48, then the value of ab + bc + ca is _______.
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
a + b + c = 10 and a2 + b2 + c2 = 4
Concept Used:
(a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
Calculation:
⇒ Using the formula (a + b + c)2 we get,
⇒ (a + b + c)2 = a2 + b2 + c2 + 2ab + 2bc + 2ca
⇒ (10)2 = 48+ 2(ab + bc + ca)
⇒ 100 – 48 = 2(ab + bc + ca)
⇒ ab + bc + ca = \(\frac{52}{2}\) = 26
Therefore, the value of ab + bc + ca is 26.
Last updated on Jun 17, 2025
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