If a , b , c are positive real numbers such that

```
a(b+c) = 32
b(c+a) = 65
c(a+b) = 77
```

Find the value of a*b*c

0 votes

If a , b , c are positive real numbers such that

```
a(b+c) = 32
b(c+a) = 65
c(a+b) = 77
```

Find the value of a*b*c

+2 votes

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 .

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