Question

formulate a quadratic equation so as to divide 16 into two parts such that twice show the square of the larger part exceeds the square of the smaller part by 164.please formulate the quadratic equation​

Answer 1

Answer:

Step-by-step explanation:

Let x and (16 - x) are two parts of 16 where (16 - x) is longer and x is smaller .

A/C to question,

2 × square of longer = square of smaller + 164

⇒ 2 × (16 - x)² = x² + 164

⇒ 2 × (256 + x² - 32x ) = x² + 164

⇒ 512 + 2x² - 64x = x² + 164

⇒ x² - 64x + 512 - 164 = 0

⇒ x² - 64x + 348 = 0

⇒x² - 58x - 6x + 348 = 0

⇒ x(x - 58) - 6(x - 58) = 0

⇒(x - 6)(x - 58) = 0

⇒ x = 6 and 58

But x ≠ 58 because x < 16

so, x = 6 and 16 - x = 10