Question

simplify this function. sqrt(x^2+1)+sqrt((6-x)^2+4)

Answer 1

can you do this:

y = \[\sqrt(x^2+1)+\sqrt((6-x)^2+4)\]

\[y^2 =(x^2+1)+ (6-x)^2+4\] square both sides.

y^2 = 2 x^2-12 x+41

y = \[\sqrt{2 x^2-12 x+41}\]

Answer 2

is this legit?

Answer 3

Yes, seems to be.

Answer 4

when i graph it though, via google, they look completely different

Answer 5

when you square both sides of
\(\large y= \sqrt {a}+\sqrt b\)
you DO NOT get
y= a+b, you get ,
y= \(a+b+2\sqrt{ab}\)

Answer 6

@dgamma3 Well, to sum up, \((a + b)^2 \ne a^ 2+ b^2\)

Answer 7

Yup.\[y^2 = a + b + 2\sqrt{ab}\]

Answer 8

because \((m+n)^2=m^2+n^2+\color{red}{2mn}\)

Answer 9

where am i making this mistake?

Answer 10

Going from the first to second step.

Answer 11

ok, i think i get it

Answer 12

so, to clarify