Question

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.​

Answer 1

Answer:

Let one of the number be x. Then the other number will be 2x – 3.

From the question:

x2 + (2x – 3)2 = 233

⇒ x2 + 4x2 + 9 – 12x = 233

⇒ 5x2 – 12x – 224 = 0

⇒ 5x2 – 40x + 28x – 224 = 0

⇒ 5x(x – 8) + 28(x – 8) = 0

⇒ (5x + 28) (x – 8) = 0

Now, 5x + 28 cannot be 0

so, x – 8 = 0 ⇒ x = 8

Considering the value of x = 8, we have 2x – 3 = 15

Thus, the two numbers are 8 and 15 respectively

Step-by-step explanation:

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Answer 2

the two numbers are 8 and 13.

Step-by-step explanation:

Let one of the number be x. Then the other number will be 2x – 3.

From the question:

x2 + (2x – 3)2 = 233

⇒ x2 + 4x2 + 9 – 12x = 233

⇒ 5x2 – 12x – 224 = 0

⇒ 5x2 – 40x + 28x – 224 = 0

⇒ 5x(x – 8) + 28(x – 8) = 0

⇒ (5x + 28) (x – 8) = 0

Now, 5x + 28 cannot be 0

so, x – 8 = 0 ⇒ x = 8

Considering the value of x = 8,

we have

2x – 3 = 2(8) - 3 = 16-3 = 13 .

Thus, the two numbers are 8 and 13.

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