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3 years ago

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

Mathematics

1 answer:

marissa [1.9K]3 years ago

8 0

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).

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