**Student:** sonu yadav

**Q. Solve question 6x¼-x½=9**

**Answer : **

Hi Sonu, Nice question.

Here is the explanation how to solve this kind of problems.

Topic : Algebra - Equation and Simplication

**Question : 6x ^{1/4} - x^{1/2} = 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.

**6x ^{1/4} - x^{1/2} = 9**

On observing the question, what if we substitute x^{1/4} with something !!

Let's substitute **x ^{1/4 }= t**

On substituting, equation becomes :

6(t) - (t)^{2} = 9

On removing brackets 6t - t^{2} = 9

On re-arranging to form quadratic equation, we get

t^{2} - 6t + 9 = 0

On factorizing t^{2} - 6t + 9

Splitting middle term t^{2} - 3t -3t + 9

we get (t - 3) (t -3) = 0

Hence t = 3

On re-substituting, **x ^{1/4 }= t**

we get **x ^{1/4 }= 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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