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    What is the possible value of (a + b + c) – 3, if a² +b² +c² = 9 and ab + bc + ca = 8?
    Question

    What is the possible value of (a + b + c) – 3, if a² +b² +c² = 9 and ab + bc + ca = 8?

    A.

    5

    B.

    3

    C.

    9

    D.

    2

    Correct option is D

    Given:
     a² +b² +c² = 9 and  ab + bc + ca = 8.
    To find: value of  (a + b + c) – 3 
    Formula Used:  
    (a+b+c)2=a2+b2+c2+2(ab+bc+ac)(a + b + c)^2 = a^2 + b^2 +c^2 +2(ab+bc+ac)  
    Solution: 
    Putting the values in formula;

    (a+b+c)2=9+2×8(a+b+c)2=9+16a+b+c=25a+b+c=5So,(a+b+c)3=53=2(a+b+c)^2 = 9 + 2 \times 8 \\(a+b+c)^2 = 9 + 16 \\ a+b+c = \sqrt {25} \\ a+b+c = 5 \\ \text{So,} \\ (a+b+c)-3 = 5-3 = 2  

    Alternate Method:

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