### 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 :    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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