Question

Find the value of expression a² + b² + c², if a+b+c= 9 and 1 by a plus 1 by b plus 1 by c=0​

Answer 1

Explanation:

Given, a + b + c = 9 and 1/a + 1/b + 1/c = 0

Multiplying both sides by abc, we get:

bc + ac + ab = 0

Multiplying both sides by 2 and adding (a+b+c)^2 to both sides, we get:

2(bc + ac + ab) + (a+b+c)^2 = (a^2 + b^2 + c^2) + 2(ab + bc + ac) + 81

Simplifying and substituting bc + ac + ab = 0, we get:

(a^2 + b^2 + c^2) = 81

Therefore, the value of a^2 + b^2 + c^2 is 81

Answer 2

Explanation:

We can use the following identities to simplify the expression we need to find:

(a+b+c)^2 = a^2 + b^2 + c^2 + 2ab + 2ac + 2bc

(a+b+c)(1/a+1/b+1/c) = 3 + (ab+bc+ac)/abc

From the second equation, we can substitute the value given for 1/a + 1/b + 1/c = 0:

(a+b+c)(0) = 3 + (ab+bc+ac)/abc

0 = 3

This is a contradiction, so there is no solution that satisfies both equations. Therefore, the value of a^2 + b^2 + c^2 cannot be determined with the information given.