Question

(e) If a +b+c= 12 and a² +62 +62 = 64, find the value of ab + bc + ac.​

Answer 1

Answer:

ab + bc + ac = 40

Step-by-step explanation:

We have,

a + b + c = 12 ----- 1

a² + b² + c² = 64 ----- 2

Now, Let's square eq.1,

(a + b + c)² = 12²

Using the identity,

(x + y + z)² = x² + y² + z² + 2(xy + yz + xz)

a² + b² + c² + 2(ab + bc + ac) = 144

From eq.2 we get,

(a² + b² + c²) + 2(ab + bc + ac) = 144

64 + 2(ab + bc + ac) = 144

2(ab + bc + ac) = 144 - 64

2(ab + bc + ac) = 80

ab + bc + ac = 80/2

ab + bc + ac = 40

Hence,

ab + bc + ac = 40

Hope it helped and believing you understood it....All the best