Answer:
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)
=<em> </em><em>5</em>0 - 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).
