Given a+b+c=7 and a^2+b^2+c^2=25 Find (a+b) ^2 + (a+c) ^2 + (b+c) ^2

26.

Step-by-step explanation:

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

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

= 50 - 2 (ab + ac + bc) ... (1).

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

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

= 25 + 2 (ab + ac + bc)

But (a + b + c) ^2 = 7^2 = 49. So:-

49 = 25 + 2 (ab + ac + bc)

2 (ab + ac + bc) = 49 - 25 = 24.

Substituting for this in (1) above:

(a + b) ^2 + (a + c) ^2 + (b + c) ^2 = 50 - 24 = 26 (answer).