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Question 29

The square root of a number plus $$2$$ gives the number itself. Then the number is


Correct Answer: 4

Solution

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Let the number be $$N$$ 

We are given that $$\sqrt{N}+2 = N$$

Let us substitute $$y=\sqrt{N}$$ to obtain a quadratic. 

Then we can rewrite the equation as 

$$y+2=y^2 \implies y^2-y-2=0$$

Factorising the equation we get

$$(y-2)(y+1)=0$$. 

Since $$y=\sqrt{N}$$, it is non-negative hence we get

 $$y=2$$ and $$N=y^2 = 4$$.

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