Question

Consider the equation
(2x - 1) (2x - 3) (2x -5) (2x - 7) = 945.
Find the sum of all integer solutions for X.

Answer 1

Answer:

(2x - 1)( 2x - 7) (2x - 3)(2x - 5) = 945

⇒ ( 4x² - 16 x + 7)( 4x² - 16 x +15) = 945

Let 4 x² - 16 x be t

⇒ (t + 7)(t + 15) = 945

⇒ t² + 22t + 105-945=0

⇒ t² + 22 t - 840 = 0

⇒ t² + 42t - 20t - 840=0

(t - 20)(t + 42)=0

t= 20,-42

4 x² - 16x + 42=0

⇒ 2x² - 8x + 21 = 0

No integer solutions here.

4 x² - 16 x = 20

⇒ x² - 4 x - 5=0

⇒ (x - 5)(x + 1)=0

x = - 1 and 5

Answer 2

Step-by-step explanation:

Option A: (17,15) Factor that divides both of them is 1.

Option B: (10,16) Factors that divides both oh them are 1,2.

Option C: (20,24) Factors that divide both of them are 1,2,4.

Option C: (31,62) Factors that divide both oh them are 1,31.

In reference to above definition (17,15) are co-prime numbers.