-
The sum of squares of three positive integers is 323. If the sum of squares of two numbers is twice the third, their product is
-
- 255
- 260
- 265
- 270
Correct Option: A
Let the positive numbers be x, y and z (respectively).
∴ x2 + y2 + z2 = 323 ... (i)
and x2 + y2 = 2z ... (ii)
∴ z2 + 2z = 323
⇒ z2 2z – 323 = 0
⇒ z2 + 19z – 17z – 323 = 0
⇒ z (z + 19) – 17 (z + 19) = 0
⇒ (z – 17) (z + 19) = 0
⇒ z = 17 because z ≠ –19
∴ x2 + y2 = 2 × 17 = 34
= 32 + 52
∴ xyz = 3 × 5 × 17 = 255
