How do you solve 4= sqrt x - 3root4x?

2 Answers
Cem Sentin
Mar 14, 2018

x=4^4=256

Explanation:

4= sqrtx - 3root4x

Set y=root4x, sqrtx became y^2. Hence,

y^2-3y=4

y^2-3y-4=0

(y-4)*(y+1)=0

So y_1=-1 and y_2=4

But x=(-1)^4=1 doesn't provide equation. Thus,

x=4^4=256 is solution of it.

Ratnaker Mehta
Mar 14, 2018

" The Soln. Set "sub RR" is "{256}.

Explanation:

We will solve the eqn. in RR.

Letting, root(4)x=t, x=t^4 :. sqrtx=t^2.

Substituting in the given eqn., we get,

4=t^2-3t, or, t^2-3t-4=0.

:. ul(t^2-4t)+ul(t-4)=0.

:. t(t-4)+1(t-4)=0.

:. (t-4)(t+1)=0.

:. t=4, or, t=-1.

:. x=t^4=4^4=256, or, x=(-1)^4=1.

But, we observe that, x=1 does not satisfy the original eqn.

:." The Soln. Set "sub RR" is "{256}.

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