Student: sonu yadav
Q. Solve question 6x¼-x½=9
Hi Sonu, Nice question.
Here is the explanation how to solve this kind of problems.
Topic : Algebra - Equation and Simplication
Question : 6x1/4 - x1/2 = 9 Solve for x.
Concept : Since the equation contains powers in fractions, this type of problems can be solved by making the question as simple as possible.
Method with Explanation:
As mentioned in concept above, lets see how we can make this equation simple.
6x1/4 - x1/2 = 9
On observing the question, what if we substitute x1/4 with something !!
Let's substitute x1/4 = t
On substituting, equation becomes :
6(t) - (t)2 = 9
On removing brackets 6t - t2 = 9
On re-arranging to form quadratic equation, we get
t2 - 6t + 9 = 0
On factorizing t2 - 6t + 9
Splitting middle term t2 - 3t -3t + 9
we get (t - 3) (t -3) = 0
Hence t = 3
On re-substituting, x1/4 = t
we get x1/4 = 3
On squaring both sides 2 times :
we get x = 3 * 3 * 3 * 3
Hence x = 81
Hope you understood and likes the method and explanation.
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