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The sum of the squares of two positive numbers is greater than their product by 2 8 . If the ratio of the numbers 2 : 3 , find th e numbers .
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- 4 and 6
- 6 and 9
- 8 and 12
- None of these
Correct Option: A
Let the numbers be 2x and 3x.
∴ (3x)2 + (2x)2 2 – 2x × 3x = 28
⇒ 13x2 – 6x2 = 28
⇒ 7x2 = 28
| ⇒ x2 = | ; 4 | |
| 7 |
⇒ x = √4 = 2
∴ Numbers are : 4 and 6
