Question

If a2 + b2 + c2 = 75, and (ab – bc – ca) = 75 find the value of (a – b – c)..

Answer 1

Answer:

Here is the solution to this problem…..

The given equations are:

a (a + b + c) = 45 …….(i)

b (a + b + c) = 75 ……..(ii)

c (a + b + c)= 105 …….(iii)

Adding (i), (ii) and (iii), we get:

(a + b + c) (a + b + c) =45 + 75 + 105

i.e. (a + b + c)^2 = 225

Taking square root on both sides of above eqn., we get:

(a + b + c) = 15

Put the value of (a + b + c) in eqn.s (i), (ii) and (iii), we get:

a × 15 = 45

b × 15 = 75

c × 15 = 105

This implies that

a = 3, b = 5, c = 7

So, we have

(a^2 + b^2 + c^2) = 3^2 + 5^2 + 7^2

= 9 + 25 + 49

=83. :-

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