the sum of six timesa number and four times the reciprocal of same number is 14.find the number
6 n + 4/n = 14 ???
6 n^2 + 4 = 14 n
6 n^2 - 14 n + 4 = 0
3 n^2 - 7 n + 2 = 0
(3n-1)(n-2)= 0
n = 1/3 or 2
which do you think?
Hint - try 2
then try 1/3 :)
i think it is like this way
let one number be x
and its reciprocal be 1/x
6x + 4/x = 14
since x is down i multiply it throughout the equation
like this way
x X 6x + x X 4/x = 14
then the equation is like this
6x2 + 4 = 14x
6x2 + 14x = 4
then we have to do factorisation method and i got answer that is
x=2/6 x=2
its a ssc sum
To find the number, let's set up an equation based on the information given.
Let the number be represented by "x".
According to the given information, the sum of six times the number and four times the reciprocal of the same number is 14. We can write this as an equation:
6x + 4(1/x) = 14
To solve this equation, we'll first simplify the expression:
6x + 4/x = 14
To eliminate the fraction, we'll multiply every term by x:
6x^2 + 4 = 14x
Now, let's rearrange the equation to bring it to a quadratic form:
6x^2 - 14x + 4 = 0
To solve this quadratic equation, we can factor or use the quadratic formula. In this case, factoring may be a bit challenging, so let's use the quadratic formula:
The quadratic formula is:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 6, b = -14, and c = 4. Plugging these values into the quadratic formula, we get:
x = (-(-14) ± √((-14)^2 - 4(6)(4))) / (2(6))
Simplifying further:
x = (14 ± √(196 - 96)) / 12
x = (14 ± √100) / 12
x = (14 ± 10) / 12
Solving for both possible values:
x1 = (14 + 10) / 12 = 24 / 12 = 2
x2 = (14 - 10) / 12 = 4 / 12 = 1/3
Therefore, the possible values for the number are x = 2 and x = 1/3.