Answer:
x = 3 or x = 7
Explanation:
Let's represent the unknown number as "x." According to the given information, the sum of the number and 21 times its reciprocal is 10.
Mathematically, we can express this as:
x + 21 * (1/x) = 10
To solve this equation, we can first eliminate the fraction by multiplying through by x:
x^2 + 21 = 10x
Rearranging the equation:
x^2 - 10x + 21 = 0
Now, we have a quadratic equation. To solve for x, we can factorize or use the quadratic formula
In this case, we can factorize the equation as:
(x - 3)(x - 7) = 0
Setting each factor equal to zero:
x - 3 = 0 or x - 7 = 0
Solving for x:
x = 3 or x = 7
Therefore, the possible values for the number are x = 3 or x = 7.