Two whole numbers are in ratio 3:2. If the sum of their square is 52, the numbers are: 1. 9 and 6 2. 6 and 4 3. 9 and 4 4. none of these

6 and 4 Reason It is given that two whole numbers are in ratio 3:2. Let the numbers be 3x and 2x. The sum of their square = 52. ⇒ (3x)2 + (2x)2 = 52 ⇒ 9x2 + 4x2 = 52 ⇒ 13x2 = 52 ⇒ x2 = ⇒ x2 = 4 ⇒ x = ⇒ x = 2 So, the numbers = 3x = 3 x 2 or 3 x (-2) = 6 or -6 2x = 2 x 2 or 2 x (-2) = 4 or -4 Since, the given numbers are whole numbers. So, the numbers cannot be -6 and -4. Hence, option 2 is the correct option.

Mathematics

Two whole numbers are in ratio 3:2. If the sum of their square is 52, the numbers are:
9 and 6
6 and 4
9 and 4
none of these

Quadratic Equations

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Answer

6 and 4

Reason

It is given that two whole numbers are in ratio 3:2.

Let the numbers be 3x and 2x.

The sum of their square = 52.

⇒ (3x)² + (2x)² = 52

⇒ 9x² + 4x² = 52

⇒ 13x² = 52

⇒ x² = $\dfrac{52}{13}$

⇒ x² = 4

⇒ x = $\sqrt{4}$

⇒ x = $\pm$ 2

So, the numbers = 3x = 3 x 2 or 3 x (-2) = 6 or -6

2x = 2 x 2 or 2 x (-2) = 4 or -4

Since, the given numbers are whole numbers. So, the numbers cannot be -6 and -4.

Hence, option 2 is the correct option.

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Two whole numbers are in ratio 3:2. If the sum of their square is 52, the numbers are:
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Quadratic Equations

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