Question

a+b=2009, find the value of (-1)+(-1)
inn in nositive integers x?+y?-​

Answer 1

Step-by-step explanation:

Solution :-

a² - b⁴ = 2009

a² - b⁴ = (a + b²)(a - b²)

 

Now, we have to find out all the factors of 2009.

Factors of 2009 are = 1, 7, 41,49, 287  and 2009

Now, we have to use the difference of squares of factorization to obtain (a + b²)(a - b²) = 2009

The prime factorization of 2009 is 7²*41.

If we choose two factors 'x' and 'y' such that xy = 2009,

a + b² = x and a - b² = y, then 2b² = x - y. 

If x = 2009, then y = 1 and 2b² = 2008,

then, b² = 2008/2

b = √1004 which is not and integer.

Now, if x = 287, then y = 7 and 2b² = 280

then, b² = 280/2

b = √140 which is also not an integer.

Now, if x = 49, then y = 41 and 2b² = 8

then b² = 8/2

b = √4

b = 2

Now, putting the value of b =2 in a² - b⁴ = 2009

⇒ a² - 2⁴ = 2009

⇒ a² - 16 = 2009

⇒ a² = 2009 + 16

⇒ a² = 2025

⇒ a = √2025

⇒ a = 45

So, the value of a and b is 45 and 2 respectively.

Answer 2

Answer:

(-1) + (-1) = 1 + 1

a+b=2009

then, 1 + 1 = 2

x+2=2009

x=2009-2

x=2007

Step-by-step explanation:

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