can sum1 pls help me!?
the value of x satisfying √(x+1) - √(x-1) =1 is
a. 5/4
b. 1/2

Question

anonymous · Answer

$$\sqrt{x+1} - \sqrt{x-1}=1$$

anonymous · Answer

ok for this problem, we need to isolate one of the radical terms. Your first step would be to add root x-1 to both sides of the equation

anonymous · Answer

first square the equation
x+1 + x-1 +2sqrt(x^2-1)=1
2x+2sqrt(x^2-1)=1
2sqrt(x^2-1)=1-2x
square again
4(x^2-1)=1+4x^2-4x
-4=1-4x
4x=5
x=5/4.

anonymous · Answer

tnx a lot...shud v do (a +b ) ^2 ?

anonymous · Answer

yeah (a+b)^2=a^2+b^2+2ab

anonymous · Answer

so will it be 2x +2$$\sqrt{x ^{2 -1}} = 1$$

anonymous · Answer

Or just directly substitute the options in the equation and see which satisfies...
like if you substitue 1/2 you have a sqrt(x-1)=sqrt(-1/2) which is not defined so 1/2 is wrong
now sqrt(5/4 -1) -sqrt(5/4 +1)= sqrt(9/4)-sqrt(1/4)=3/2 -1/2 =1 so 5/4 is the answer

anonymous · Answer

yep...thank u .. :)