Divide 16 into two part such that twice the square of larger part is m

1.	Divide 16 into two part such that twice the square of larger part is more, then 164 from the square of the smaller part.
Answer» Let larger part be x Smaller part = 16 – x According to question, 2x² = (16 – x)² + 164 ⇒ 2x² – (16 – x)² – 164 = 0 ⇒ 2x² – [256 – 32x + x²] – 164 = 0 ⇒ 2x² – 256 + 32x – x² – 164 = 0 ⇒ x² + 32x – 420 = 0 ⇒ x² + 42x – 10x – 420 = 0 ⇒ x(x + 42) – 10(x + 42) = 0 ⇒ (x + 42) (x – 10) = 0 ⇒ x = -42 or x = 10 ⇒ x = 10 [x = -42 not possible] Larger number (x) = 10 Smaller number (16- x) = 16 – 10 = 6 Hence two numbers are 10, 6

Divide 16 into two part such that twice the square of larger part is more, then 164 from the square of the smaller part.

Answer»

Let larger part be x

Smaller part = 16 – x

According to question,

2x² = (16 – x)² + 164

⇒ 2x² – (16 – x)² – 164 = 0

⇒ 2x² – [256 – 32x + x²] – 164 = 0

⇒ 2x² – 256 + 32x – x² – 164 = 0

⇒ x² + 32x – 420 = 0

⇒ x² + 42x – 10x – 420 = 0

⇒ x(x + 42) – 10(x + 42) = 0

⇒ (x + 42) (x – 10) = 0

⇒ x = -42 or x = 10

⇒ x = 10 [x = -42 not possible]

Larger number (x) = 10

Smaller number (16- x) = 16 – 10 = 6

Hence two numbers are 10, 6