Question

divide 16 into two parts such that two times the square of larger part is 164 more than the square of smaller part ​

Answer 1

Answer:

Step-by-step explanation:

Solution:-

given by:-

divide 16 into two parts let x is longer part and

(16-x ) is smaller part

acourdind to quetion:-

2 \times  {x}^{2}  =  {(16 - x)}^{2}  + 164 \\ 2 {x}^{2}  = 256 +  {x}^{2}  - 32x + 164 \\  {x}^{2}  + 32x - 420  = 0\\  {x}^{2}  + 42x  - 10x - 420 = 0 \\ x(x + 42) - 10(x + 42)  = 0\\ (x + 42)(x - 10) = 0 \\ x =  - 42 \: does \: not \: exits \\ (x = 10 ) \: longer \: part \\ (16 - x) = (16 - 10) \\ 6 \: is \: smaller \: part \\ 10 \: is \: longer \: part \\  

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Answer 2

Answer:

y = 6 and x = 10

Step-by-step explanation:

Let the two parts be x and y.

∴ x + y = 16

∴ x = 16 - y   --------------- 1

According to the question,

2(x²) = 164 + y²

2(16 - y)² = 164 + y²

2(256 + y² - 32y) = 164 + y²

512 + 2(y²) - 64y = 164 + y²

y² - 64y + 348 = 0

y² - 6y - 58y + 348 = 0

y (y-6) - 58 (y-6) = 0

(y-58) (y-6) = 0

∴ y = 58    or     y = 6  ----------------- 2

Substituting 2 in 1

If y = 58,

x = 16 - 58

∴ x = -42

if y = 6

x = 16 - 6

x = 10

(Neglecting the negative value)

y = 6

x = 10