The difference between a number and its reciprocal is 7/12. Find the number.
Let's represent the number as "x".
According to the given information, the difference between the number and its reciprocal is 7/12.
The equation for this can be written as:
x - 1/x = 7/12
To solve this equation, we can multiply both sides by 12x to remove the denominators:
12x(x) - 12(1) = 7x
Simplifying further, we get:
12x^2 - 12 = 7x
Rearranging the equation to have all terms on one side:
12x^2 - 7x - 12 = 0
Factoring the equation, we have:
(3x + 4)(4x - 3) = 0
Setting each factor equal to zero:
3x + 4 = 0 or 4x - 3 = 0
Solving for x in each equation:
3x = -4 or 4x = 3
x = -4/3 or x = 3/4
Therefore, the possible values for the number are -4/3 and 3/4.
To find the number, let's start by assigning a variable. Let's call the number "x".
According to the given information, the difference between a number (x) and its reciprocal (1/x) is equal to 7/12.
So, we can write the equation as:
x - (1/x) = 7/12
To solve this equation, we can first simplify by getting rid of the denominator by multiplying through by 12x:
12x * (x - (1/x)) = 12x * (7/12)
This simplifies to:
12x^2 - 12 = 7x
Now, let's rearrange the equation by bringing all terms to one side:
12x^2 - 7x - 12 = 0
This is a quadratic equation in standard form. To solve it, we can factor it or use the quadratic formula. In this case, let's use factoring.
We need to find two numbers that multiply to give -144 (12 * -12) and add up to give -7.
After some trial and error, we find that the numbers are -16 and 9:
(4x - 3)(3x + 4) = 0
Now, we can set each factor equal to zero and solve for x:
4x - 3 = 0
4x = 3
x = 3/4
and
3x + 4 = 0
3x = -4
x = -4/3
So, there are two possible solutions: x = 3/4 and x = -4/3.
Therefore, the number could be either 3/4 or -4/3.
*so a - (1/a) =(7/12)
Multiply both sides from 12a to get,
12(a^2) - 12 =7a
Let the number be a ,so its reciprocal is (1/a)
Multiplying both sides by 12a we get,
So a - (1/a) = 7/12
12(a^2) - 12 = 7a
12(a^2) - 7a - 12 =0
Now solve for a.