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The sum of three positive numbers is 18 and their product is 162. If the sum of two numbers is equal to the third number, then the sum of squares of the numbers is
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- 120
- 126
- 132
- 138
Correct Option: B
Let three positive integers be x, y and z.
According to the question,
x + y + z = 18 ..... (i)
xyz = 162 ..... (ii)
and x + y = z ..... (iii)
From equation (i),
z + z = 18 ⇒ 2z = 18 ⇒ z = 9
∴ xyz = 162
⇒ xy × 9 = 162
| ⇒ xy = | = 18 ..... (iv) | |
| 9 |
∴ (x – y)2 = (x + y)2 – 4xy
= (9)2 – 4 × 18
= 81 – 72 = 9
∴ x – y = 3
∴ x + y + x – y = 9 + 3
⇒ 2x = 12 ⇒ x = 6
∴ x + y + z = 18
⇒ 6 + y + 9 = 18
⇒ y = 18 – 15 = 3
∴ x2 + y2 + z2
= (6)2 + (3)2 + (9)2
= 36 + 9 + 81 = 126
