Question

if a,b,c are positive deals such that a(b+c) =32, b(c+a)=65 and c(a+b)=72 then a×b×c= ……………​

Answer 1

Answer:

Step-by-step explanation:

a(b+c) = 32 .....ab + ac = 32 so I get bc - ac = 33

b(c+a) = 65.......bc + ab = 65 ac - ab = 12

c(a+b) = 77.......ac + bc = 77 bc - ab = 45

so, ac + bc + bc - ac = 77 + 33 so, bc = 55

ab + ac + ac - ab = 32 + 12 ac = 22

bc + ab - bc + ab = 65 - 45 ab = 10

so a*b*c = squareroot of ( 10 * 22 * 55 ) = 110 .

OR OTHER METHOD

Step 1: Solving the equation gives

ab = 10

bc = 55

ac = 22

Step 2: multiply these three equations

ab*bc*ac = 10*55*22

Step 3: taking the squareroot

abc = 110