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If (x+y+z)(y+z-x)(z+x-y)(x+y-z) prop x^2...

If `(x+y+z)(y+z-x)(z+x-y)(x+y-z) prop x^2y^2` then show that either `x^2+y^2= z^2` or `x^2+y^2-z^2 prop xy`.

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UNITED BOOK HOUSE-MISCELLANEOUS EXERCISE-EXERCISE
  1. If (a+c):(b+c) = (a/b+2):(b/a+2) then show that (a-c):(b-c) = a^2:b^2.

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  2. If (5a-3b)/a= (4a+b-2c)/(a+4b-2c) = (a+2b-3c)/(4a-4c), then show that ...

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  3. If (x+y+z)(y+z-x)(z+x-y)(x+y-z) prop x^2y^2 then show that either x^2+...

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  4. If 1/x-1/y prop 1/(y-x) then show that x/y is constant.

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  5. Simplify: 1/sqrt(11-2sqrt(30))-3/(sqrt7-2sqrt(10))-4/(sqrt(8+4sqrt3))

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  6. Find the square roots of- 8+2sqrt2-2sqrt5-2sqrt(10)

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  7. Find the square roots of- 1+x^2+ sqrt(1+x^2+x^4)

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  8. If 2x = sqrta+1/sqrta. Show that sqrt(x^2-1)/(x-sqrt(x^2-1))(a-1)

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  9. If (x+sqrt(x^2-bc))(y+sqrt(y^2-ca))(z+sqrt(z^2-ab)) = (x-sqrt(x^2-bc...

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  10. If x = (sqrt(a^2+b^2)+sqrt(a^2-b^2))/(sqrt(a^2+b^2)-sqrt(a^2-b^2)) sho...

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  11. If x>y prove that sqrt(y+sqrt(2xy-x^2))+sqrt(y-sqrt(2xy-x^2)) = sqrt(...

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  12. Solve for x, when sqrt(2x^2 + 9) + sqrt(2x^2 - 9) = 9 + 3sqrt7

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  13. Solve: (a+x)^(2//3)+2(a-x)^(2//3) = 3(a^2-x^2)^(1//3)

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  14. Find the area of a sector of a circle with radius 6 cm if angle of the...

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  15. If x prop y+z , y propz+x and z prop x+y, and the constant of variat...

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  16. If x,y,z be variable quantities such that (x+y+z) is constant and (z+x...

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  17. If x/y alphax+y and y/x alpha x-y, then show that x^2-y^2= constant.

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  18. The radii of two circles are 8 cm and 6 cm respectively. Find the diam...

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  19. If ax+by prop sqrt(xy), then show that (ax)^2+(by)^2 prop xy,

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  20. If y prop 1/x then show that x+y will be minimum when x=y.

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