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Prove that (x-a)^2/((a-b)(a-c))+(x-b)^...

Prove that
`(x-a)^2/((a-b)(a-c))+(x-b)^2/((b-a)(b-c))+(x-c)^2/((c-a)(c-b))=1`

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KALYANI PUBLICATION-HARDER PRODUCT AND FACTORISATION -EXERCISE
  1. If x-y=7and xy=9, then find the value of (x^2+y^2)

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  2. Prove that 4x^2(y-z)+y^2(2x-z)+z^2(2x+y)-4xyz = (2x+y)(y-z)(2x-z)

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  3. Prove that (x-a)^2/((a-b)(a-c))+(x-b)^2/((b-a)(b-c))+(x-c)^2/((c-a)(...

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  4. Prove that 1/(a(a-b)(a-c))+1/(b(b-c)(b-a))+1/(c(c-a)(c-b))=1/(abc)

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  5. Prove that a/(bc(a-b)(a-c))+b/(ca(b-c)(b-a))+c/(ab(c-a)(c-a))=1/(abc...

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  6. Prove that 2(s-a)(s-b)(s-c)+a(s-b)(s-c)+b(s-c)(s-a)+c(s-a)(s-b)=abc ...

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  7. Factorise a^3-b^3+1+3ab

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  8. If a + b + c = 0, then prove that 1/(2a^2+bc)+1/(2b^2+ca)+1/(2c^2+a...

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  9. If a^2 + b^2 + c^2 -ab-bc-ca = 0, then prove that a=b=c

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  10. If a + b + c = 0, then prove that (a+b)^2/(ab) + (b+c)^2/(bc) + (c+...

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  11. If a + b + c = 0, then prove that (2a^2)/(a^2-b^2-c^2)+(2b^2)/(b^2-...

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  12. If a + b + c = 0, then prove that (a^2+b^2+c^2)/(a^3+b^3+c^3)+2/3(1...

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  13. If a+b=c then prove that 1/(b^2+c^2-a^2)+1/(c^2+a^2-b^2)+1/(a^2+b^2...

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  14. If a+b+c=0, then prove that a(c+a)(a+b)=b(a+b)(b+c)=c(a+c)(b+c)=abc

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  15. If a+b+c=0, then prove that a(b+c)^2+b(c+a)^2+c(a+b)^2=3abc

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  16. If A=ax+by+cz, B=bx+cy+az, C=cx+ay+bz and a+b+c=0, then prove that A...

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  17. If x^(1/3)+y^(1/3)+z^(1/3)=0, then prove that (x+y+z)^3=27xyz

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  18. If a+b+c=0, then prove that a^4+b^4+c^4=2(ab+bc+ca)^2

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  19. If a+b+c=0, then prove that (a^2+b^2+c^2)^2=4 (a^2b^2+b^2c^2+c^2a^2)

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  20. If a+b+c=0, then prove that a(b+c)^2+b(c+a)^2+c(a+b)^2=3abc

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