Question

A positive number is divided into two parts such that the sum of the squares of the two parts is 208. Square of larger numberr is 88 times the smaller part. Taking x as smaller part of the two parts, find the number.

Answer 1

Answer:

The required number is 16.553

Step-by-step explanation:

Given:

• A positive number is divided into two parts such that the sum of the squares of the two parts is 208.
• Square of larger numberr is 88 times the smaller part.

To find:

• The number.

Solution:

Let the two parts in which the number is divided be x and y and y be the bigger number.

According to the problem,

• x² + y² = 208
• y = 208 - x² ...1

• y² = 88 × x
• y² = 88x ...2

Now, substitute the value of 1 in eq2, we get:

• 208 - x² = 88x
• 208 - x² - 88x = 0
• - x² - 88x + 208 = 0

Use quadratic formula to solve the equation,

✰ ( - b ± √b² - 4ac )/2a

Where,

a = - 1

b = - 88

c = 208

• = ( - 1 × - 88 ± √- 88² - 4 × - 1 × 208 )/2 × - 1
• = ( - 1 × - 88 ± √- 88² - 4 × - 208 )/2 × - 1
• = ( - 1 × - 88 ± √7744 + 832 )/2 × - 1
• = ( - 1 × - 88 ± √7744 + 832 )/2 × - 1
• = ( - 1 × - 88 ± √- 8576 )/2 × - 1
• = ( 88 ± √- 8576 )/-2

We will take positive value after solving for x, we have:

• x = 2.303

Now, find y by substituting the value of x into y, we have:

• y² = 88 × 2.303
• y² = 202.664
• y = √202.664
• y = 14.25

Finally,

The required number = 2.303 + 14.25

The required number ≈ 16.553

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