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three numbers are such that their sum is 50, product is 3750 and the sum of their reciprocals is 31/50 .Find the sum of the squares of the three numbers.
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- 2500
- 1250
- 950
- 122
Correct Option: C
x + y + z = 50 ; xyz = 3750
| ∴ | + | + | = | ||||
| x | y | z | xyz |
| = | |
| 150 |
| ⇒ xy + yz + zx = | xyz | |
| 150 |
| = | × 3750 = 775 | |
| 150 |
∴ (x + y + z )2 = x2 + y2 + z2 + 2(xy + yz + zx)
⇒ (50)2 + x2 + y2 + z2 + 2 × 775
⇒ 2500 = x2 + y2 + z2 + 1550
⇒ x2 + y2 + z2 = 2500 – 1550
= 950
