# If the ratio of the roots of #lx^2+nx+n = 0# is #p/q# then how do you prove that #(p/q)^(1/2)+(q/p)^(1/2)-(n/l)^(1/2) = 0# ?

See explanation...

Then:

So equating coefficients, we find:

Then:

So taking the principal square root of both sides, we have:

I rushed through "taking the principal square root of both sides" without explaining it properly.

There are a couple of cases to consider:

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When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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