Question

If a and b are whole numbers such that ab = 2027 find the value of a+b. Explain your answer.​

Answer 1

Step-by-step explanation:

∵ a - b is a whole number 

As, if a is a whole number and b is a whole number then a+b,a-b,ab is a whole number except a/b

Answer 2

The value of (a+b) is √( a² + b² + 4054).

Step-by-step explanation:

According to the given information, it is given that, a and b are whole numbers and the value of ab is given as 2027.

We need to find the value of a + b.

Now, we know that the well - known algebraic identity, that is,

the square of (a + b)² is equal to the sum of the squares of a and b and the term 2ab, that is, (a + b)² = a² + b² + 2ab.

Let this be equation 1.

Now, from equation 1, we get that, (a+b)² = a² + b² + 2(2027).

Or,  (a+b)² = a² + b² + 4054.

Thus, (a+b) = √( a² + b² + 4054)

Thus, the value of (a+b) is √( a² + b² + 4054)...(2)

Now, a*b = 2027. Now, since 2027 is a prime number, the only factors of  2027 are 1 and the number itself. Thus, a must be 1 and b must be 2027.

Thus, equation 2 gives, (a+b) = √( 1 + 2027² + 4054) = 2028.

thus, the value of a + b = 2028.

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