Question

Divide 16 into two parts such that twice the square of the large part exceeds the square of the smaller part by 164

Answer 1

Let the smaller part be x

The larger part is 16 - x

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STEP 1: Form the equation:

The square of the larger part exceed the square of the smaller part by 164

(16 - x)² - x² = 164

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STEP 2: Solve x:

(16 - x)² - x² = 164

Apply (a - b)² = a² - 2ab + b² :

256 - 32x + x² - x² = 164

Combine like terms:

-32x + 256 = 164

Subtract 256 from both sides:

-32x = -92

Multiply both sides by -1:

32x = 92

Divide both sides by 3:

x = 2.875

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STEP 3: Find the numbers:

smaller part = x = 2.875

bigger part = 16 - x = 13.125

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Answer: The numbers are 2.875 and 13.125

Answer 2

Refers to attachment.....