Question

The sum of the squares of two natural numbers is 34. If the first number is one less than
twice the second number, find the number.

Answer 1

Let the first number be x . Therefore the second number will be 2x-1 . Now ATQ , x^2 + (2x-1)^2= 34 x^2 + 4.x^2 +1 - 4.x =34 5.x^2 - 4.x +1 -34=0. 5.x^2 -4.x-33=0. 5.x^2 -15x +11x-33=0. 5x(x-3)+11(x-3)=0. (5x+1)(x-3)=0. Therefore , 5x +1=0. or. x-3 =0. Therefore x=-1/5 or x =3 as we have to take only natural numbers .So x=3. Hence the numbers will be x=3 & 2x-1 = 6-1=5