If (x - 9)1/2 + 2 = (x - 2)1/2?

Question

what is X?

Answer 1

assuming the 1/2 at the end of each parenthetical does mean 1/2 of the resulting expression, the equation can be rewritten as follows (for the sake of simplicity): (x - 9)/2 + 2 = (x - 2)/2

Solve for x as follows:
(x - 9)/2 + 2 = (x - 2)/2
x/2 - 9/2 + 2 = x/2 - 2/2
x/2 - 5/2 = x/2 - 1
x/2 - x/2 = 5/2 - 1
0 = 3/2

Because 0 does not equal 3/2, there is no solution.

Answer 2

You can use the carrot (^) to raise to a power. ...
No problem, so we have:
(x - 9)^1/2 + 2 = (x - 2)^1/2
Rearranging:
(x - 2)^1/2 - (x - 9)^1/2 = 2 (eqn 1)
The form is:
a - b = 2
Knowing that:
(a-b)(a+b) = a^2 - b^2
Multiply LHS of eqn 1 by unity, where unity is written:
[(x - 2)^1/2 + (x - 9)^1/2]/[(x - 2)^1/2 + (x - 9)^1/2]
We get:
[(x - 2) - (x - 9)]/[(x - 2)^1/2 + (x - 9)^1/2] = 2
Or:
7/[(x - 2)^1/2 + (x - 9)^1/2] = 2 (eqn 2.)
Let:
a = (x - 2)^1/2
b = (x - 9)^1/2
From eqn.1:
a - b = 2
From eqn. 2:
7/[a + b] = 2
Or:
a + b = 3.5
Two eqns and two unknowns:
b = .75 = (x - 9)^1/2
a = 2.75 = (x - 2)^1/2
Only one of the above is needed to solve for x:
x = 9.5625

Fun in the sun!

Answer 3

if :
1/2(x-9)+2=1/2(x-2)then :we multiply by 2 then we got :
(x-9)+4=(x-2)
x-9+4=x-2
x-5=x-2)
x-x=5-2
0=3
this equation is impossible

Answer 4

x/2 - 9/2 + 2 = x/2 - 2/2
mmc = 2
x/2 - 9/2 + 4 = x/2 - 1
x/2 - x/2 = -1 + 9/2 -4
There is no value for X.
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Answer 5

1/2x -4+2=1/2x-1

multiply by common denominator

x-8+2=x-2

x-x=8-2



no solution