We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33⇒ a−b =33 and a+b=61
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33⇒ a−b =33 and a+b=61Solving for a and b, we get
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33⇒ a−b =33 and a+b=61Solving for a and b, we geta=47,b=14
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33⇒ a−b =33 and a+b=61Solving for a and b, we geta=47,b=14∴ab=658
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So, (a + b) * (a – b) = 2013
Since, both a and b are natural numbers;
so, (a – b) and (a + b) are natural numbers too and,(a + b) > (a – b)
Now the factors of 2013 are: 1, 3, 11, 61 and 2013
From the above factors;
four probable combinations are possible.
They are (1, 2013), (3, 671), (33, 61) and (11, 183).If (a – b) = 1 and (a + b) = 2013;
a = 1007 and b = 1006;
so, ab = 1013042
If (a – b) = 3 and (a + b) = 671;
a = 337 and b = 334;
so, ab = 112558
If (a – b) = 11 and (a + b) = 183; a = 97 and b = 86;
so, ab = 8342
If (a – b) = 33 and (a + b) = 61; a = 47 and b = 14;
so, ab = 658
So, the minimum value of ab = 658
We can write 2013+a
We can write 2013+a 2
We can write 2013+a 2 =b
We can write 2013+a 2 =b 2
We can write 2013+a 2 =b 2 as
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33⇒ a−b =33 and a+b=61
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33⇒ a−b =33 and a+b=61Solving for a and b, we get
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33⇒ a−b =33 and a+b=61Solving for a and b, we geta=47,b=14
We can write 2013+a 2 =b 2 as(b+a)(b−a)=2013Factorising 2013(b+a)(b−a)=3×11×61In our case the product of ab is minimum, when the difference between the numbers is minimum. From our factors the minimum product of any two numbers from the given factors is 11×3=33⇒ a−b =33 and a+b=61Solving for a and b, we geta=47,b=14∴ab=658
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