When is <msqrt> x <mrow class="MJX-TeXAtom-ORD"> / </mrow> y 2

Grimmingch

Grimmingch

Answered question

2022-05-28

When is x / y 2 equal to x / y?
The solution to the quadratics is given by
r = b 2 a ± b 2 4 a c 4 a 2 , which is shortened to r = b 2 a ± b 2 4 a c 2 a , but I'm wondering how if this is justified, given that 4 a 2 can be negative if a C , and x y x y if x and y are negative, but given that we have a 2 , is this justified?
Is x / y 2 = x / y? Is r = b 2 a ± b 2 4 a c 2 a always true?

Answer & Explanation

Syllingbs

Syllingbs

Beginner2022-05-29Added 11 answers

When y > 0, you have
x y 2 = x y 2 = x y .
When y < 0, you have
x y 2 = x y 2 = x y .
uznosititr

uznosititr

Beginner2022-05-30Added 3 answers

The two possible values of 4 a 2 for complex a differ only by a sign (one is 2 a, the other is 2 a), so the set of solutions given by the formula
r = b 2 a ± b 2 4 a c 2 a
is the same as that given by the formula
r = b 2 a ± b 2 4 a c 4 a 2 .
(The "plus" in one formula may or may not correspond to "plus" in the other one, but this doesn't matter.)

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