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If x=7+4sqrt(3)\ \ a n d\ x y=1 , then 1...

If `x=7+4sqrt(3)\ \ a n d\ x y=1` , then `1/(x^2)+1/(y^2)=`? (a) 64 (b) 134 (c) 194 (d) `1/(49)`

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To solve the problem, we need to find the value of \( \frac{1}{x^2} + \frac{1}{y^2} \) given that \( x = 7 + 4\sqrt{3} \) and \( xy = 1 \). ### Step-by-Step Solution 1. **Identify the values of \( x \) and \( y \)**: - We know \( x = 7 + 4\sqrt{3} \). - Since \( xy = 1 \), we can express \( y \) as: \[ ...
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RD SHARMA-RATIONALISATION -All Questions
  1. The rationalisation factor of 2+sqrt(3) is (a) 2-sqrt(3) (b) sqrt(2...

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  2. If x=sqrt(5)+\ 2, then x-1/x equals (a)2sqrt(5) (b) 4 (c) 2 (...

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

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  4. The simplest rationalising factor of root(3)(500) is 2 3 (b) 5 3 ...

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  5. The simplest rationalising factor of sqrt(3)+ sqrt(5) is (a)sqrt(3)-5...

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  6. The simplest rationalising factor of 2sqrt(5)-sqrt(3) is (a)2sqrt(5)+...

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  7. If x=2/(3+sqrt(7)) , then (x-3)^2= 1 (b) 3 (c) 6 (d) 7

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  8. If x=7+4sqrt(3)\ \ a n d\ x y=1 , then 1/(x^2)+1/(y^2)=? (a) 64 ...

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  9. If x+ sqrt(15)=4, then x+1/x= 2 (b) 4 (c) 8 (d) 1

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  10. If x=root(3)(2+sqrt(3)) , then x^3+1/(x^3)= 2 (b) 4 (c) 8 (d) 9

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  11. If x=(sqrt(5)+\ sqrt(3))/(sqrt(5)-\ sqrt(3)) and y=(sqrt(5)-\ sqrt(3))...

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  12. If x=(sqrt(3)-\ sqrt(2))/(sqrt(3)+sqrt(2)) and y=(sqrt(3)+\ sqrt(2))/(...

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  13. The value of sqrt(3-2\ sqrt(2)) is sqrt(2)-1 (b) sqrt(2)+1 (c)...

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  14. The value of sqrt(5+2sqrt(6)) is sqrt(3)-sqrt(2) (b) sqrt(3)+sqrt(2...

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  15. If sqrt(2)=1. 4142 , then sqrt((sqrt(2)-1)/(sqrt(2)+1)) is equal to 0....

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  16. If sqrt(2)=1. 414 find the value of sqrt(3)\/ sqrt(6) upto three place...

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  17. The positive square root of 7+sqrt(48)

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  18. 1/(sqrt(9)- sqrt(8)) is equal to: (a)3+2sqrt(2) (b) 1/(3+2sqrt(2)...

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  19. The value of (sqrt(48)+ sqrt(32))/(sqrt(27)+ sqrt(18)) is (a)4/3 ...

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  20. If x=sqrt6+sqrt5 then x^2+1/x^2-2=

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