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If x+1/x=3, then x^6+1/(x^6)=? (a)927 ...

If `x+1/x=3,` then `x^6+1/(x^6)=?` (a)927 (b) 414 (c) 364 (d) 322

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To solve the problem where \( x + \frac{1}{x} = 3 \) and we need to find \( x^6 + \frac{1}{x^6} \), we can follow these steps: ### Step 1: Square the given equation We start with the equation: \[ x + \frac{1}{x} = 3 \] Now, we square both sides: ...
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RD SHARMA-ALGEBRAIC IDENTITIES-All Questions
  1. If x+1/x=2, then x^3+1/(x^3)=? (a)64 (b) 14 (c) 8 (d) 2

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  2. If x+1/x=4, then x^4+1/(x^4)=? (a)196 (b) 194 (c) 192 (d) 190

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  3. If x+1/x=3, then x^6+1/(x^6)=? (a)927 (b) 414 (c) 364 (d) 322

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  4. If x^4+1/(x^4)=623 , then x+1/x=? (a)27 (b) 25 (c) 3sqrt(3) (d) ...

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  5. If x^2+1/(x^2)=102 , then x-1/x=? (a)8 (b) 10 (c) 12 (d) 13

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  6. If x^3+1/(x^3)=110 , then x+1/x=? (a)5 (b) 10 (c) 15 (d) none of ...

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  7. If x^3-1/(x^3)=14 , then x-1/x=? (a)5 (b) 4 (d) 3 (d) 2

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  8. If x^4+1/(x^4)=194 , find x^3+1/(x^3),x^2+1/(x^2) and x+1/x

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  9. If x-1/x=(15)/4, then x+1/x\ =? (a)4 (b) (17)/4 (c) (13)/4\ (d...

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  10. If 3x+2/x=7, then (9x^2-4/(x^2))=? (a)25 (b) 35 (c) 49 (d) 30

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  11. If a^2+b^2+c^2-a b-b c-c a=0, then a+b=c b+c=a c+a=b a=b=c

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  12. If a+b+c=0 , then (a^2)/(b c)+(b^2)/(c a)+(c^2)/(a b)=?\ (a)0 (b) ...

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  13. If a^(1/3)+\ b^(1/3)+\ c^(1/3)=0 then (a)a+b+c=0 (b) (a+b+c)^3=27\ a...

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  14. If a+b+c=9 and a b+b c+c a=23 , then a^2+b^2+c^2=? (a)35 (b) 58 (c)...

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  15. If a+b+c=9 and a b+b c+c a=23 , then a^3+b^3+c^3-3a b c=? (a)108 (b) ...

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  16. (a-b)^3 + (b-c)^3 + (c-a)^3=? (a)(a+b+c)(a^2+b^2+c^2-ab-bc-ac) (b)3(...

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  17. Simplify: ((a^2-b^2)^3+(b^2-c^2)^3+(c^2-a^2)^3)/((a-b)^3+(b-c)^3+(c-a)...

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  18. The product (a+b)(a-b)(a^2-a b+b^2)(a^2+a b+b^2) is equal to: (a)a^6+b...

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  19. If a/b+b/a=\ -1, then a^3-b^3=? (a)1 (b) -1 (c) 1/2 (d) 0

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  20. The product (x^2-1)(x^4+x^2+1) is equal to: (a)x^8-1 (b) x^8+1 (...

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