Home
Class 12
MATHS
If x, y are rational numbers such that (...

If x, y are rational numbers such that `(x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1)sqrt(5)` then

A

`x=1,y=1`

B

`x=2,y=1`

C

`x=5,y=1`

D

x & y can take infinitely many values

Text Solution

AI Generated Solution

Promotional Banner

Topper's Solved these Questions

  • DEFINITE INTEGRATION & ITS APPLICATION

    RESONANCE ENGLISH|Exercise High Level Problem|26 Videos

  • EQUATIONS

    RESONANCE ENGLISH|Exercise EXERCISE-2 (PART-II: PREVIOUSLY ASKED QUESTION OF RMO) |5 Videos

Similar Questions

Explore conceptually related problems

If the A.M. and G.M. between two numbers are in the ratio x:y , then prove that the numbers are in the ratio (x+sqrt(x^(2)-y^(2))):(x-sqrt(x^(2)-y^(2))) .

Assuming that x , y are positive real numbers, simplify each of the following: (i) sqrt(x^(-2)y^3) (ii) (x^(-2)doty^(-1/2))^2 (iii) (sqrt(x^(-3)))^5

The complex numbrs x and y such that x,x+2y,2x+y are n A.P. and (y+1)^2, xy+5, (x+1)^2 are in G.P. are (A) x=3, y=1 (B) x=-1+2sqrt(2)i, y=1/3 (-1+2sqrt(2)i) (C) x=sqrt(2)+i, y=3sqrt(5)-sqrt(2)i (D) x=-1(1+2sqrt(2)i), y= - 1/3 (1+2sqrt(2)i)

Let f (x,y)= x^(2) - y^(2) and g (x,y)=2xy. such that (f ( x,y))^(2) -(g (x,y))^(2)=1/2 and f (x,y) . G(x,y) =(sqrt3)/(4) Find the number of ordered pairs (x,y) ?

Assuming that x , y , z are positive real numbers, simplify each of the following: (i) (sqrt(x))^(-2/3)\ \ sqrt(y^4)\ -:\ sqrt(x y^(-1/2))

If x is very large as compare to y , then prove that sqrt(x/(x+y))dotsqrt(x/(x-y))=1+(y^2)/(2x^2) .

The solution of (x d x+y dy)/(x dy-y dx)=sqrt((1-x^2-y^2)/(x^2+y^2)) is

The locus of P(x,y) such that sqrt(x^2+y^2+8y+16)-sqrt(x^2+y^2-6x+9)=5, is

Find x and y if: (3/sqrt(5) x-5)+i2 sqrt (5) y= sqrt(2)

If 0 (a) sqrt(x)-\ sqrt(y)=\ sqrt(x-y) (b) sqrt(x)+\ sqrt(x)=\ sqrt(2x) (c) xsqrt(y)=ysqrt(x) (d) sqrt(x y)=\ sqrt(x)\ sqrt(y)

RESONANCE ENGLISH-DPP-QUESTION
  1. Find the value of 'a', if (x - a) is a factor of x^(3)-ax^2+x+2.

    Text Solution

    |

  2. If 2x^(3)-5x^(2)+x+2=(x-2)(ax^(2)-bx-1), then a & b are respectively :

    Text Solution

    |

  3. If x, y are rational numbers such that (x+y)+(x-2y)sqrt(2)=2x-y+(x-y-1...

    Text Solution

    |

  4. Write the following sets in Roaster form : (i) A={x:x" is a natural ...

    Text Solution

    |

  5. Write of the following sets in the set builder from : {:((i),{1},(ii...

    Text Solution

    |

  6. Are the following of sets equal ? (i) {x:x is a letter in the word '...

    Text Solution

    |

  7. If x/a=y/b=z/c, then show that (x^3+a^3)/(x^2+a^2)+(y^3+b^3)/(y^2+b^2)...

    Text Solution

    |

  8. If |{:(x^(2)-2x+3,7x+2,x+4),(2x+7,x^(2)-x+2,3x),(3,2x-1,x^(2)-4x+7):}|...

    Text Solution

    |

  9. If 1/3(log)3M+3(log)3N=1+(log)(0. 008)5, then

    Text Solution

    |

  10. (log)3(1+1/3)+(log)3(1+1/4)+(log)3(1+1/5)+ddot+(log)3(1+1/(242)) when...

    Text Solution

    |

  11. Solve ((x-5)^(2)(x+2)^(3)(x-4))/((x-3)^(4))le0

    Text Solution

    |

  12. Which of the following sets are equal ? A={x:x inN,xlt4},B=(1,1,2,3,...

    Text Solution

    |

  13. Find the power set of the set {a,b,c}.

    Text Solution

    |

  14. Let A={1,2,3,5},B={1,2,3}andC={1,2,5}. Find all the sets X satisfying ...

    Text Solution

    |

  15. Let A={phi,{phi},2,{2,phi},3}, which of the following are true ? {:((...

    Text Solution

    |

  16. Remove the irrationality in the denominator a. sqrt((sqrt(2)-1)/(sq...

    Text Solution

    |

  17. Solve the following inequations {:((i),(x-2)/(x^(2)-9)lt0,(ii),(x+1)(...

    Text Solution

    |

  18. If a+b+c=2,a^(2)+b^(2)+c^(2)=1 and abc = 3 then 1/a+1/b+1/c is equal t...

    Text Solution

    |

  19. If 3x=a+b+c , then the value of (x-a)^3+\ (x-b)^3+\ (x-c)^3-3\ (x-a)(x...

    Text Solution

    |

  20. Which of the following when simplified reduces to unity? (log)(3/2)(l...

    Text Solution

    |