(a+b)^1/2=(a-b)^-1/2 how do you solve this?

Answer 1

start by squaring both sides: (remember that a+b≥0 and a-b>0)

(a+b)=(a-b)^(-1)

a+b=1/(a-b)

(a+b)(a-b)=a^2-b^2 = 1

a^2 = 1+b^2

a=±√(1+b^2) (But a≥-b and a≥b so a≥|b|≥0) so we can throw out the negative

so a=√(1+b^2) (and you don't have to worry about a-b being 0 since a=√(1+b^2)>b)

Answer 2

The answers above have not solved for a and b

Square both sides:

then we have (a+b) = (a-b)^(-1)

multiply both sides by a-b and we have:

(a+b)(a-b)=(a-b)^0

then we have a^2 - b^2 = 1

Now, for no matter what we choose for a and b, a^2>=0 and b^2>=0

and, since we need a^2 - b^2 to have a difference of one, the only possible way we can do this is 1-0 (since any squares of integers <-1 or >1 will give us a greater difference than 1 or a lesser difference than -1).

Hence, the solution set is {(1,0),(-1,0)} (if equivalence cannot be imaginary, the solution (-1,0) should be removed)

Q.E.D.

Answer 3

A lot of guys above me have done it right but just one prob is that

a^2-b^2 is an equation of a hyper bola so it cannot be solved further. That is there is no need to find out the value of a and b unless another equation is given

Answer 4

Solve,

(a+b)^1/2 = (a-b)^-1/2

Square both sides,

[(a + b)^1/2]^2 = [(a - b)^-1/2]^2

(a + b) = (a - b)^-1

(a + b)(a - b) = 1

a^2 - b^2 = 1

a^2 = b^2 + 1

Therefore, a = sqr(b^2 + 1) or a = - sqr(b^2 +1)

Answer 5

start with all things in parenthasis then the multiplication then the devision then the addition the subtraction

a+b^1/2=a-b^-1/2

a+b /2 = -a+b/2

Answer 6

That equation is already solved my friend.... it is just showing you the relationship between the two sides. Do this.......... Substitute both a's with 2, and substitute both b's with 5. Then just solve each side individually........ guess what you'll get??? The same value on either side......

Answer 7

(a+b)^1/2 =(a-b)-1/2
(a+b)^1/2 =1/(a-b)1/2
squaring both sides
(a+b) =1/(a-b)
now
(a+b)(a-b) = 1
a^2 - b^2 = 1

Answer 8

(a + b)^(1/2) = (a - b)^(-1/2)
(a + b)^(1/2) = 1/((a - b)^(1/2))
a + b = 1/(a - b)
(a + b)(a - b) = 1
a^2 - b^2 = 1
a^2 = b^2 + 1
a = sqrt(b^2 + 1)
-b^2 = -a^2 + 1
b^2 = a^2 - 1
b = sqrt(a^2 - 1)

ANS :
a = sqrt(b^2 + 1)
b = sqrt(a^2 - 1)

Answer 9

It's a koan...a Zen riddle with no real answer.

Answer 10

I believe it needs more information!