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The sum of the squares of two numbers is 233 and one of the numbers is 3 less than twice the other number. Find the numbers.

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9,12

4,14

8,13

0,12

answer is C.

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Detailed Solution

Given,
The sum of the squares of two numbers is 233.
Consider the numbers are Integers and one of the numbers is

x

.
So, the other number will be

2 x − 3

.
Then according to the question,

x 2 + 2 x − 3 2 = 233 … . (1)

Convert equation (1) to the product of two linear factors. Question Image

Comparing two linear factors from equation (2) with zero.
⇒

x - 8 = 0

5 x + 28 = 0

⇒

x = 8, - \frac{28}{5}

Since, x cannot be a rational number or fraction as numbers are considered to be an integer.
Therefore,

x = 8

Substitute the value of x in the equation (1),
Another number

= (2 x − 3)

⇒ 2 (8) − 3 ⇒ 16 − 3 ⇒ 13

Thus, the numbers are 8 and 13 and the correct option is 3.

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