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(a) (i) By taking any two irrational n...

(a) (i) By taking any two irrational numbers, prove that their sum is a rational number.
(ii) By taking any two irrational numbers, prove that their difference is a rational number.
(b) Insert in between ` 1/7 and 2/7`
(i) a rational number : (ii) an irrational number.

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The correct Answer is:
`1/7 and 2/7`
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CALCUTTA BOOK HOUSE-REAL NUMBERS -Exercise 1.4 ( Long answer)
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  2. If E be a random experiment or rolling a dice and S be its sample spac...

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  3. If sqrt((sqrt10 +1)/(sqrt10-1)) then find the value of (x 1/x)

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  4. IF x =13 + 2sqrt(42) then find the value of ( sqrtx - 1/sqrt(x))

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  5. simplify : (a) sqrt(98) + sqrt(8) -2 sqrt(32) (b) (sqrt3 + sqrt5...

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  6. Find the value of (a)(3sqrt2)/(sqrt3 + sqrt6) - (4sqrt3)/(sqrt6 + sq...

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  7. Simplify : (a) sqrt(y+sqrt(2xy-x^(2))) + sqrt(y-sqrt(2xy-x^(2))) (b)...

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  8. If a = sqrt5 + 2 then find the value of : a^(2) + 1/a^(2)

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  9. If x = 1/(2-sqrt3) then find the value of (x^(3) -2x^(2) -7x+2)

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  10. If a x = 2 + sqrt3 then evaluate (x^(3) -5x^(2) + 5x + 9)

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  11. If a = (sqrt3-1)/(sqrt3+1) and ab=1 , then find (a^3 + b^3)

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  12. If a = (sqrt3+1)/(sqrt3-1) and ab=1 , then find (a^(2) + ab + b^(2))

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  13. If a = (sqrt5 +1 )/(sqrt5-1) and b = (sqrt5-1)/(sqrt5+1) then deter...

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  14. If x = (2sqrt15)/(sqrt5 + sqrt3) then evaluate (x+sqrt3)/(x-sqrt3) +...

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  15. If x= (sqrt5+1)/(sqrt5-1) and x = 1/y then find the value of (3x^(...

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  16. If a = (sqrt5 +1)/(sqrt5-1) and b = (sqrt5-1)/(sqrt5+1) then find the...

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  17. If x= 1/(2+sqrt3) and y = 1/(2-sqrt3) then evalue (1/(x+1) + 1/(y...

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  18. Prove that sqrtx/(sqrtx +sqrty) + sqrty/(sqrtx-sqrty) + (2sqrt(xy))/(...

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  19. Prove that 1/(1+sqrt2) + 1/(sqrt2 +sqrt3) + 1/(sqrt3+sqrt4) + 1/(sqrt4...

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