Question

11. There are 3 positive whole numbers, the product of first and second number is
24, product of second and third number is 48 and that of first and third is 32;
let's calculate to find the three numbers.​

Answer 1

Answer:

There is much more elegant solution:

xy = 24, (1)

yz = 48, (2)

xz = 32. (3)

Multiply all three equations (both sides). You will get

x%5E2%2Ay%5E2%2Az%5E2 = 24*48*32, or

xyz = +/- sqrt%2824%2A48%2A32%29, or

xyz = +/- 24%2A8 = +/- 192. (4)

Now divide equation (4) by the equation (1) (both sides). You will get

z = +/- 8.

Next divide equation (4) by the equation (2) (both sides). You will get

x = +/- 4.

Finally, divide equation (4) by the equation (3) (both sides). You will get

y = +/- 6

Answer. There are TWO solutions: a) (x,y,z) = (4,6,8), and b) (x,y,z) = (-4,-6,-8).