Question

√x+4=x. find the value of x
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Answer 1

Answer:

We have x÷4=4÷x.

If x≠0, then we multiply both sides with x.

x²÷4=4⇔x²=16⇔x²=4²⇔√(x²)=√(4²)⇒x=±4.

If x=0, the equation does not have a solution, as we get 0÷4=4÷0, where 4÷0 is undefined. If we try to solve it with limits, we get,

limx→0+(x÷4)=limx→0+(4÷x)⇒0=+∞ (false).

As one of the side limits doesn’t solve the equation, the other side limit will either lead to the same equation (which if we try to solve it, it won’t) or give a different value which means that the limx→0 doesn’t exist at all for this equation.

So the only solutions to this equation are either 4 or -4.