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If xyz=1 then show that (1+x+y^-1)^-1+(1...

If xyz=1 then show that `(1+x+y^-1)^-1+(1+y+z^-1)^-1+(1+z+x^-1)^-1=1 `

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The correct Answer is:
`(1)/((1 + y + xy)(1 + z + yz)(1 + x + zx))`
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CBSE COMPLEMENTARY MATERIAL-NUMBER SYSTEMS-Part - D
  1. Express 0.6 + 0.overline(7) + 0. overline(47) in the form (p)/(q) wher...

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  2. Rationalise the denominator of (1)/(sqrt(3)+sqrt(5)+sqrt(7))

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  3. Find the value of a and b if (7+3sqrt(5))/(3+sqrt(5))-(7-3sqrt(5))...

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  4. If x = (3 - 2 sqrt(2)), show that (sqrt(x) - (1)/(sqrt(x))) = +- 2

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  5. If xyz=1 then show that (1+x+y^-1)^-1+(1+y+z^-1)^-1+(1+z+x^-1)^-1=1

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  6. Find the value of x if (i) 25^(2x - 3) = 5^(2x + 3) (ii) (4)^(2x...

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  7. Evaluate: (64^((a)/(6)))/(4^(a))times(2^(2a+1))/(2^(a-1))

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  8. Show that: 1/(1+x^(b-a)+x^(c-a))+1/(1+x^(a-b)+\ x^(c-b))+1/(1+x^(b-c)+...

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  9. Simplify: (x^a/x^(-b))^(a-b)xx(x^b/x^(-c))^(b-c)xx(x^c/x^(-a))^(c-a)

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  10. Let T = (1)/(3-sqrt(8))-(1)/(sqrt(8)-sqrt(7)) +(1)/(sqrt(7)-sqrt(6))-(...

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  11. If a=(sqrt(7)-sqrt(6))/(sqrt(7)+sqrt(6)) and b=(sqrt(7)+sqrt(6))/(sqrt...

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  12. (2sqrt(6))/(sqrt(2)+sqrt(3))+(6sqrt(2))/(sqrt(6)+sqrt(3))-(8sqrt(3))/(...

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  13. If x=9−4sqrt5 then , find the value of [x^3− 1/(x^3)]

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  14. If a=1+sqrt(7) , find the value of -6/a

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  15. If p=5-2sqrt(6) Find p^(2)+(1)/(p^(2))

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  16. Express 0.3178 is the form of p/q where p and q are integers

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  17. If sqrt(2) = 1.414 then find the value of sqrt(8) + sqrt(50) + sqrt(72...

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  18. Simplify: 4/((216)^(-2/3))+1/((256)^(-3/4))+2/((243)^(-1/5))

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