SOLUTION: Find the value of A and B if sqrtA * sqrtB = 4 sqrtA

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Question 1118066: Find the value of A and B if
sqrtA * sqrtB = 4
sqrtA - sqrtB = sqrt8
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) (Show Source):
You can put this solution on YOUR website!
I think someone solved this one but may have left some work for you the student. I will do all the steps but you should try to understand them if you expect to learn this.
(1)
(2)
(1) �>
Substitute RHS of this for in (2):

Here I let

Complete the square: add to both sides. Note that so we are simply adding 2 to both sides:

Re-write, and move the 4 to the RHS:

Take square root of both sides:

(*)

Squaring this gives B:

Using (*) and (2): �>

Squaring this gives A:

�
Check:
(ok)
(ok)

Answer by ikleyn(52781) (Show Source):
You can put this solution on YOUR website!
.
This problem can be solved in more simple way.

Let x be the value (now unknown) exactly half-way between and , i.e. x = . So then = x + = x + , = x - = . Then from = 4 you get = 4, or = 4, which is the same as = 4, which implies = 4 + 2 = 6; hence, x = . Then = ====> square both sides ====> A = = . = ====> square both sides ====> B = = .

SOLUTION: Find the value of A and B if sqrtA * sqrtB = 4 sqrtA - sqrtB = sqrt8