Given an integer N, the task is to find two numbers a and b such that a * b = N and a + b = N. Print “NO” if no such numbers are possible.
Examples:
Input: N = 69
Output: a = 67.9851
b = 1.01493Input: N = 1
Output: NO
Approach: If observed carefully, we are given with sum and product of roots of a quadratic equation.
If N2 – 4*N < 0 then only imaginary roots are possible for the equation, hence “NO” will be the answer. Else a and b will be:
a = ( N + sqrt( N2 – 4*N ) ) / 2
b = ( N – sqrt( N2 – 4*N ) ) / 2
Below is the implementation of the above approach:
C++
// C++ program to find a and b // such that a*b=N and a+b=N #include <bits/stdc++.h> using namespace std; // Function to return the smallest string void findAandB(double N) { double val = N * N - 4.0 * N; // Not possible if (val < 0) { cout << "NO"; return; } // find a and b double a = (N + sqrt(val)) / 2.0; double b = (N - sqrt(val)) / 2.0; cout << "a = " << a << endl; cout << "b = " << b << endl; } // Driver Code int main() { double N = 69.0; findAandB(N); return 0; } |
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Java
// Java program to find a and b // such that a*b=N and a+b=N class GFG{ // Function to return the smallest string static void findAandB(double N) { double val = N * N - 4.0 * N; // Not possible if (val < 0) { System.out.println("NO"); return; } // find a and b double a = (N + Math.sqrt(val)) / 2.0; double b = (N - Math.sqrt(val)) / 2.0; System.out.println("a = "+a); System.out.println("b = "+b); } // Driver Code public static void main(String[] args) { double N = 69.0; findAandB(N); } } // This Code is contributed by mits |
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Python3
# Python 3 program to find a and b # such that a*b=N and a+b=N from math import sqrt # Function to return the # smallest string def findAandB(N): val = N * N - 4.0 * N # Not possible if (val < 0): print("NO") return # find a and b a = (N + sqrt(val)) / 2.0 b = (N - sqrt(val)) / 2.0 print("a =", '{0:.6}' . format(a)) print("b =", '{0:.6}' . format(b)) # Driver Code if __name__ == '__main__': N = 69.0 findAandB(N) # This code is contributed # by SURENDRA_GANGWAR |
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C#
// C# program to find a and b // such that a*b=N and a+b=N using System; class GFG { // Function to return the smallest string static void findAandB(double N) { double val = N * N - 4.0 * N; // Not possible if (val < 0) { Console.WriteLine("NO"); return; } // find a and b double a = (N + Math.Sqrt(val)) / 2.0; double b = (N - Math.Sqrt(val)) / 2.0; Console.WriteLine("a = "+a); Console.WriteLine("b = "+b); } // Driver Code static void Main() { double N = 69.0; findAandB(N); } // This code is contributed by ANKITRAI1 } |
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PHP
<?php // PHP program to find a and b // such that a*b=N and a+b=N // Function to return the // smallest string function findAandB($N) { $val = $N * $N - 4.0 * $N; // Not possible if ($val < 0) { echo "NO"; return; } // find a and b $a = ($N + sqrt($val)) / 2.0; $b = ($N - sqrt($val)) / 2.0; echo "a = " , $a, "\n"; echo "b = " , $b, "\n"; } // Driver Code $N = 69.0; findAandB($N); // This code is contributed by ajit ?> |
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Output:
a = 67.9851 b = 1.01493
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