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If a + b + c = 0 , then prove that a^(3...

If a + b + c = 0 , then prove that `a^(3)+b^(3)+c^(3)=3abc`

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CALCUTTA BOOK HOUSE-FACTORISATION-EXERCISE 2.4 (Short -answer type questions )
  1. If a + b + c = 0 , then prove that a^(3)+b^(3)+c^(3)=3abc

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  2. Prove that (x^(201)+1) is divisible by (x+1).

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  3. If a = 1 , b = 2 , c = 3 , then find then value of (2a^(2)+2b^(2)+2c^...

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  4. Show that (17^(3)+7^(3)) is divisible by 24.

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  5. If a + b + 1 = 0 , determine the value of (a^(3)+b^(3)-3ab+1).

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  6. If a = b = c = 99999 , then find the value of (a^(3)+b^(3)+c^(3)-3abc)

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  7. If a + b + c = 8 and ab + bc + ca = 11 , then find the value of a^(3)+...

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

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  9. If a^(2)-b^(2)=224 where a and b are negative integers (a lt b) the...

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  10. If c be a whole number , but not a natural number and if (a^(2))/(b)+(...

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  11. Find the value of (0.01)^(3)-(0.011)^(3)+(0.001)^(3)+0.00000033

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  12. Find : ((b^(2a)-c^(2a))^(3)+(c^(2a)-a^(2a))^(3)+(a^(2a)-b^(2a))^(3))/(...

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  13. If 3s = a + b + c , then find (s-a)^(3)+(s-b)^(3)+(s-c)^(3)+3(s-a)(s-b...

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  14. Calculate : (80)^(3)-(20)^(3)-(60)^(3)

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  15. Calculate : (10^(3)+4^(3))/(10^(2)-24)

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  16. If a + b +5 = 0 , then find the value (a^(3)+b^(3)-15ab+125)

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  17. If a - b = - 1 then find the value of (a^(3)-b^(3)+3ab+1)

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  18. If ane0, determine the number of factors of ka^(2)-(27)/(a)

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  19. If x-kx^(2)+4 = (x+1) (x-a) be an identity , then find the value of k...

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  20. If a and b be two positive integers (agtb) such that a^(2)-b^(2)=39...

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