Home
Class 12
MATHS
If x,y in R satisfy the equation x^2 + y...

If `x,y in R` satisfy the equation `x^2 + y^2 - 4x-2y + 5 = 0,` then the value of the expression `[(sqrtx-sqrty)^2+4sqrt(xy)]/((x+sqrt(xy))` is

Text Solution

Verified by Experts

The correct Answer is:
`(sqrt(2 + 1))/(sqrt(2))`
`f(x, y) = ( x - 2)^(2) + (y - 1)^(2) = 0`
`rArr x = 2 and y = 1`
`therefore ((sqrt(x) - sqrt(y))^(2) + 4 sqrt(xy))/(x + sqrt(xy))`
= ` (sqrt(2 -1)^(2) + 4sqrt(2)^(2))/(2 + sqrt(2)) =(sqrt(2) + 1)^(2)/(sqrt(2)(sqrt 2 + 1)) = (sqrt(2) + 1)/(sqrt(2))`
Promotional Banner

Topper's Solved these Questions

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.9|12 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.10|5 Videos

  • THEORY OF EQUATIONS

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 2.7|9 Videos

  • STRAIGHT LINES

    CENGAGE PUBLICATION|Exercise ARCHIVES (NUMERICAL VALUE TYPE)|1 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

Similar Questions

Explore conceptually related problems

If x ,y in R satify the equation x^2+y^2-4x-2y+5=0, then the value of the expression [(sqrt(x)-sqrt(y))^2+4sqrt(x y)]//(x+sqrt(x y)) is a. sqrt(2)+1 b. (sqrt(2)+1)/2 c. (sqrt(2)-1)/2 d. (sqrt(2)+1)/(sqrt(2))

If x^2 + 4xy + 4 = 0 , then x : y =

IF y=sin(4sin^-1x) satiesfies the relation (1-x^2)y_2-xy_1+4Ay=0 , then the value of A is -

The equation x-y=4 and x^2+4xy+y^2=0 represent the sides of

If f(x , y) satisfies the equation 1+4x-x^2=sqrt(9sec^2y+4cos e c^2y) then find the value of xtan^2ydot

(a) If x : y = 3 : 4 , then find the value of the ratio (2x + y) : ( 9x - 2y) . (b) If x : y = 5 : 4 , then find the value of the ratio (x^(2) + xy) : (x^(2) - xy) .

If x=2,y=4 , then what is the value of x+2y+sqrt((x-2y)^2) ?

If x = 2, y = 3 and z = 6 , then find the value of (3sqrtx)/(sqrty + sqrtz) - (4 sqrty)/(sqrtz + sqrtx) + (sqrtz)/(sqrtx + sqrty)

Answer any one question : x = 2 + sqrt3 and x + y = 4, then find the simplest value of xy + 1/xy.

x + y = (4)/(sqrt3) and x - y = (2)/(sqrt3) , then the value of 4xy is