If any of the three number is a perfect square , then what will be their product ?

Question

Three integers x, y, z such that 1 = < x, y ,z = < 9 and x not= y not=z are choosen. The sum of the products of number taken in pair is 73 and their sum is 16.
If any of the three number is a perfect square , then what will be their product ?

Answer 1

The number is 259 and product is 90

Answer 2

According to given conditions
xy + yz + zx = 73 and x + y + z = 16
xy + 16-(x+y) = 73
(x+y)^2 - 16(x+y) - xy + 73 = 0
(x+y)^2 - 16(x+y) - xy + 73 = 0
for y = 1, (x+1)^2 - 16(x+1) - (x+1) + 74 = 0
(x+1)^2 - 17(x+1) + 74 = 0
No integral solution of x
for y = 4, (x+4)^2 - 16(x+4) - 4x + 73 = 0
(x+4)^2 - 16(x+4) - 4(x+4) + 89 = 0
(x+4)^2 - 20(x+4) + 89 = 0
No integral solution
for y = 9, (x+9)^2 - 16(x+9) - 9x + 73 = 0
(x+9)^2 - 25(y+9) + 154 = 0
Roots are 11, 4
x + 9 = 11, x + 9 = 14
x = 2, x = 5
So numbers are 2, 5, 9
product 90

Comments

Brilliant mam