The sum of a number and its reciprocal is 2120. The number is

Given that the sum of a number and its reciprocal is 2120.A quadratic equation in the variable x is of the form ax2+bx+c=0, a≠0 where a, b and c are real numbersAnd the sum of the roots is given by –ba.Let’s consider root of the equation is m and according to the given condition its reciprocal is 1m.Sum of the roots,⟹m+1m=2120 ⟹m2+1m=4120 ⟹20(m2+1)=41m ⟹20m2+20=41m ⟹20m2-41m+20=0 Now, we will find the roots of the equation 20m2-41m+20=0 and then we will get the value of m.⟹20m2-41m+20=0⟹20m2-25m-16m+20=0⟹5m4m-5-44m-5=0⟹5m-44m-5=0⟹5m-4=0 or 4m-5=0⟹5m=4 or 4m=5∴ m=45or m=54 The required number is 45.Hence, the correct option is 1.

The sum of a number and its reciprocal is 2120. The number is

Given that the sum of a number and its reciprocal is 2120.A quadratic equation in the variable x is of the form ax2+bx+c=0, a≠0 where a, b and c are real numbersAnd the sum of the roots is given by –ba.Let’s consider root of the equation is m and according to the given condition its reciprocal is 1m.Sum of the roots,⟹m+1m=2120 ⟹m2+1m=4120 ⟹20(m2+1)=41m ⟹20m2+20=41m ⟹20m2-41m+20=0 Now, we will find the roots of the equation 20m2-41m+20=0 and then we will get the value of m.⟹20m2-41m+20=0⟹20m2-25m-16m+20=0⟹5m4m-5-44m-5=0⟹5m-44m-5=0⟹5m-4=0 or 4m-5=0⟹5m=4 or 4m=5∴ m=45or m=54 The required number is 45.Hence, the correct option is 1.