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

If `x/a=y/b=z/c,` then show that `(x^3+a^3)/(x^2+a^2)+(y^3+b^3)/(y^2+b^2)+(z^3+c^3)/(z^2+c^2)=((x+y+z)^3+(a+b+c)^2)/((x+y+z)^2+(a+b+c)^2).`

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RESONANCE ENGLISH-DPP-QUESTION
  1. Write of the following sets in the set builder from : {:((i),{1},(ii...

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  2. Are the following of sets equal ? (i) {x:x is a letter in the word '...

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

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  4. If |{:(x^(2)-2x+3,7x+2,x+4),(2x+7,x^(2)-x+2,3x),(3,2x-1,x^(2)-4x+7):}|...

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  5. If 1/3(log)3M+3(log)3N=1+(log)(0. 008)5, then

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  6. (log)3(1+1/3)+(log)3(1+1/4)+(log)3(1+1/5)+ddot+(log)3(1+1/(242)) when...

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  7. Solve ((x-5)^(2)(x+2)^(3)(x-4))/((x-3)^(4))le0

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  8. Which of the following sets are equal ? A={x:x inN,xlt4},B=(1,1,2,3,...

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  9. Find the power set of the set {a,b,c}.

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  10. Let A={1,2,3,5},B={1,2,3}andC={1,2,5}. Find all the sets X satisfying ...

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  11. Let A={phi,{phi},2,{2,phi},3}, which of the following are true ? {:((...

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  12. Remove the irrationality in the denominator a. sqrt((sqrt(2)-1)/(sq...

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  13. Solve the following inequations {:((i),(x-2)/(x^(2)-9)lt0,(ii),(x+1)(...

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  14. If a+b+c=2,a^(2)+b^(2)+c^(2)=1 and abc = 3 then 1/a+1/b+1/c is equal t...

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  15. If 3x=a+b+c , then the value of (x-a)^3+\ (x-b)^3+\ (x-c)^3-3\ (x-a)(x...

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  16. Which of the following when simplified reduces to unity? (log)(3/2)(l...

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  17. If log(6)log(2)[sqrt(4x+2)+2sqrtx]=0thenx=.

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  18. The value 'x' satisfying the equation, 4^(log(9)3)+9^(log(2)4)=10^(log...

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  19. If x=prod(n=1)^(2000)n, then the value of the expression, (1)/((1)/(l...

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  20. Simplify :""^(3)sqrt(5^((1)/(log(7)5))+(1)/(sqrt(-log(10)(0.1))))

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