What is the possible value of (a + b + c) - 3, if a2 + b2 + c2 = 9 and ab + bc + ca = 8 ?
Show answer & explanation
Correct answer: D
Explanation
The correct answer is Option 4 i.e. 2.
Given:
a2 + b2 + c2 = 9
ab + bc + ca = 8
Concept Used:
(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ac) ...(i)
Explanation:
Using the given values in the equation (i), we get
(a + b + c)2 = 9 + 2(8)
⇒ (a + b + c)2 = 9 + 16
⇒ (a + b + c)2 = 25
⇒ (a + b + c) = 5
Hence the value of (a + b + c) - 3 = 5 - 3 = 2.