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If `a : b = c : d ` , then prove that `(a + c) : (b + d) = sqrt(a^(2) - c^(2)) : sqrt(b^(2) - d^(2))`

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CALCUTTA BOOK HOUSE-RATIO AND PROPORTION-EXERCISE - 2.2 (Long Answer Type Questions)
  1. If a : b = c : d , then prove that (a + c) : (b + d) = sqrt(a^(2) - ...

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  2. If (a + b + c + d) (a - b - c + d) = (a + b - c - d) (a - b + c - d), ...

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  3. If x/y = y/z , then simplify (xyz ( x + y + z)^(3))/((xy+yz+zx)^(3))...

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  4. If a/b = c/d = e/f , then show that each ratio = ((la^(n) + mc^(n) +...

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  5. If a/b = b/c = c/d , then prove that (a^(2) + b^(2) + c^(2))(b^(2) +...

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  6. If x/(b + c) = y/(c+a) = z/(a + b), then prove that (b - c) x + (c -...

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  7. If a/(b +c) = b/(c+a) = c/(a+b) " and " a + b + c ne 0 , then prove t...

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  8. If (ay-bx)/c = (cx - az)/b = (bz - cy)/a , " then prove that " x/a = y...

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  9. If a/b = c/d ,then show that bd ((a+b)/b + (c+d)/d)^(2) = 4 (a + b) (c...

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  10. If (y+z-x)/(b+c-a) = (z+x-y)/(c+a-b) = (x+y -z)/(a + b - c)", then pro...

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

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  12. If a : b = c : d , then prove that the - proportional of (a^(2) + ...

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  13. If x/(lm - n^(2)) = y/(mn - l^(2)) = z/(nl - m^(2)) , then show that ...

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  14. If a : b = x : y , then show that (a^(2) + b^(2)) : a^(3)/(a + b) :...

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  15. If sqrtx/sqrty = (a + sqrt2)/(a - sqrt2), then find the value of (x-y...

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  16. If a/b = b/c = c/d , then show that (a - b)^(3) : (b - c)^(3) = a : d...

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  17. If b/(a + b) = (3a - c - b)/(2b + c -a) = (-a+3c)/(2a - b + 3c) ( "wh...

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  18. If a : b = c : d , then prove that (a +b)/(a - b) = sqrt(ac + ad + bc...

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  19. If (bz + cy)/a = (cx +az)/b = (ay+bx)/c, then prove that x/(a(b^(2) + ...

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