The sum of a number and four times its reciprocal is 5.Find possible values of the number.
the number --- x
its reciprocal --- 1/x
x + 4(1/x) = 5
times x
x^2 + 4 = 5x
x^2-5x + 4 = 0
(x-1)(x-4) = 0
x = 1 or x = 4
I leave it up to you to check them out.
Why did the number go to therapy? Because it felt so divided and needed to find its reciprocal!
To find the possible values of the number, let's solve the given equation step-by-step.
Step 1: Let's assume the number to be x.
Step 2: The reciprocal of x is 1/x.
Step 3: The sum of x and four times its reciprocal is given by the equation: x + 4 * (1/x) = 5.
Step 4: To solve the equation, we can multiply all terms by x to eliminate the fraction. This gives us: x^2 + 4 = 5x.
Step 5: Rearranging the equation, we get: x^2 - 5x + 4 = 0.
Step 6: We can factorize the quadratic equation: (x - 4)(x - 1) = 0.
Step 7: Setting each factor to zero, we have two possible values for x: x - 4 = 0 or x - 1 = 0.
Step 8: Solving for x in both cases gives us: x = 4 or x = 1.
Therefore, the possible values of the number are x = 4 and x = 1.
To solve this problem, we can start by assigning a variable to the unknown number. Let's call it "x".
According to the given information, the sum of the number (x) and four times its reciprocal (4/x) is equal to 5. Mathematically, we can write this as an equation:
x + 4/x = 5
To find the possible values of x, we need to solve this equation. To do so, we can multiply the entire equation by "x" to eliminate the denominator:
x(x + 4/x) = 5x
Simplifying this, we get:
x^2 + 4 = 5x
Rearranging the equation:
x^2 - 5x + 4 = 0
Now we have a quadratic equation. To solve this, we can factor it or use the quadratic formula.
Factoring:
(x - 1)(x - 4) = 0
Setting each factor equal to zero, we have two possible solutions:
x - 1 = 0 or x - 4 = 0
Solving for x, we get:
x = 1 or x = 4
Therefore, the possible values of the number are x = 1 or x = 4.