Solve the equation $r=\sqrt{a+\sqrt{a^2-16}}\sqrt{a-\sqrt{a^2-16}}$

Step-by-step Solution

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Final answer to the problem

$r=4$
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Step-by-step Solution

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  • Choose an option
  • Solve for r
  • Solve for a
  • Simplify
  • Factor
  • Factor by completing the square
  • Find the integral
  • Find the derivative
  • Find the derivative using the definition
  • Solve by quadratic formula (general formula)
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Apply the property of power of a product in reverse: $a^n\cdot b^n=(a\cdot b)^n$

Learn how to solve factor by difference of squares problems step by step online.

$r=\sqrt{\left(a+\sqrt{a^2-16}\right)\left(a-\sqrt{a^2-16}\right)}$

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Learn how to solve factor by difference of squares problems step by step online. Solve the equation r=(a+(a^2-16)^(1/2))^(1/2)(a-(a^2-16)^(1/2))^(1/2). Apply the property of power of a product in reverse: a^n\cdot b^n=(a\cdot b)^n. Solve the product of difference of squares \left(a+\sqrt{a^2-16}\right)\left(a-\sqrt{a^2-16}\right). Cancel like terms a^2 and -a^2. Calculate the power \sqrt{16}.

Final answer to the problem

$r=4$

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Function Plot

Plotting: $r-\sqrt{a+\sqrt{a^2-16}}\sqrt{a-\sqrt{a^2-16}}$

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3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

Main Topic: Factor by Difference of Squares

The difference of two squares is a squared number subtracted from another squared number. Every difference of squares may be factored according to the identity a^2-b^2=(a+b)(a-b) in elementary algebra.

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