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Given x = (sqrt(a^(2) + b^(2)) + sqrt(a...

Given `x = (sqrt(a^(2) + b^(2)) + sqrt(a^(2) - b^(2)))/(sqrt(a^(2) + b^(2)) - sqrt(a^(2) - b^(2)))`.
Use componendo and dividendo to prove that :
`b^(2) = (2a^(2)x)/(x^(2) + 1)`.

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ICSE-RATIO AND PROPORTION (INCLUDING PROPERTIES AND USES)-Exercise 7(D)
  1. If 15(2x^(2) - y^(2)) = 7xy, find x : y, if x and y both are positive...

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  2. Find the : (i) fourth proportional to 2xy, x^(2) and y^(2). (i...

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  3. Find two numbers such that the mean proportional between them is 14 an...

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  4. If x and y be unequal and x : y is the duplicate ratio of x + z and y ...

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  5. If x = (2ab)/(a + b), find the value of : (x + a)/(x - a) + (x + b)/(x...

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  6. If (4a + 9b) (4c - 9d) = (4a - 9b) (4c + 9d), prove that : a : b = c :...

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  7. If (a)/(b) = (c)/(d), show that : (a + b) : (c + d) = sqrt(a^(2) + b^...

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  8. There are 36 members in a student council in a school and the ratio of...

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  9. If 7x - 15y = 4x + y, find the value of x: y. Hence, use componendo an...

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  10. If (4m + 3n)/(4m - 3n) = (7)/(4) use properties of proportion to find ...

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  11. If x, y, z are in continued proportion, prove that : ((x + y)^(2))/((y...

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  12. Given x = (sqrt(a^(2) + b^(2)) + sqrt(a^(2) - b^(2)))/(sqrt(a^(2) + b...

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  13. If (x^(2) + y^(2))/(x^(2) - y^(2)) = 2(1)/(8), find : (i) (x)/(y)...

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  14. Using componendo and dividendo, find the value of x if (sqrt(3x+4)+sqr...

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  15. If x=(sqrt(a+1)+sqrt(a-1))/(sqrt(a+1)-sqrt(a-1)), using properties of ...

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  16. Given (x^(3)+12x)/(6x^(2)+8)=(y^(3)+27y)/(9y^(2)+27). Using componendo...

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  17. If x/(a)=y/(b)=z/(c) show that x^(3)/(a^(3))+y^(3)/(b^(3))+z^(3)/(c^(3...

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  18. If b is the mean proportion between a and c, show that : (a^(4)+a^(2...

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  19. If (7m+2n)/(7m-2n)=5/(3) use properties of proportion to find (i) m...

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  20. (i) If x and y both are positive and (2x^(2) - 5y^(2)) : xy = 1 : 3, f...

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