1.

If x+1/x=11 then √x-1/√x=​

Answer»

COMPUTING the equality,

x-1/x = 11

x-1=11x (Transposing x to RHS)

-1=11x -x

-1=10x

x= -1/10

Checking the value by substitution,

(-1/10)-1)/(-1/10)=11

(-11/10)/(-1/10)= 11

-11/10*10/-1= 11

11=11

(L.H.S = R.H.S)

Therefore, x=-1/10

((x+1)/x)^2

(((-1/10)+1)/(-1/10))^2

((9/10)/(-1/10))^2

(9/10*10/-1)^2

(-9)^2

81

So, ((x+1)/x)^2 = 81

Lets solve it in a bit DIFFERENT way, now we will convert x into decimal form, i.e -1/10= -0.1

(x^2–1)/x^2

(-0.1)^2–1/(-0.1)^2

0.01–1/0.01

-0.99/0.01

-99/100*100/1

-99

So, (x^2–1)/x^2= -99

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