A student writes the formula `sqrt(a b)=sqrt(a)\ sqrt(b)dot` Then he substitutes `a=-1\ a n d\ b=-1\ a n d\ ` finds `1=-1` . Explain where is he wrong?

If (sqrt(3)-1)/(sqrt(3)+1)=x+ysqrt(3) , find the value of x\ a n d\ y

If a=sqrt(3),b=1/2(sqrt(6)+sqrt(2))dot and c=2, then find /_A

If (sqrt(3)-\ 1)/(sqrt(3)+\ 1)=a-b\ sqrt(3) , then (a) a=2,\ b=1 (b) a=2,\ b=-1 (c) a=-2,\ b=1 (d) a=b=1

For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is 1//2 (b) 1 (c) -1 (d) 2

In a DeltaA B C ,\ if\ b=sqrt(3),\ c=1\ a n d\ /_A=30^0 , then find a

For what value of n ,\ dot(a^(n+1)+b^(n+1))/(a^n+b^n) is the arithmetic mean of a\ a n d\ b ?

In a DeltaA B C , prove the following : \ If\ a=sqrt(2),\ b=sqrt(3)\ a n d\ c=sqrt(5) , show that its area is 1/2sqrt(6) sq. units.

For the curve sqrt(x)+sqrt(y)=1 , (dy)/(dx) at (1//4,\ 1//4) is (a) 1//2 (b) 1 (c) -1 (d) 2

If vec a , vec b ,a n d vec c are such that [ vec a vec b vec c]=1, vec c=lambda vec axx vec b , angle, between vec aa n d vec b is (2pi)/3,| vec a|=sqrt(2),| vec b|=sqrt(3)a n d| vec c|=1/(sqrt(3)) , then the angel between vec aa n d vec b is pi/6 b. pi/4 c. pi/3 d. pi/2

Number of real solutions of sqrt(x)+sqrt(x-sqrt(1-x))=1 is (a) 0 (b) 1 (c) 2 (d) infinite