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Prove that a^2+b^2+c^2-a b-b c-c a is al...

Prove that `a^2+b^2+c^2-a b-b c-c a` is always non-negative for all values of `a ,b` `a nd` `c.`

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Prove that a^2+b^2+c^2-a b-b c-c a is always non-negative for all values of a ,\ b\ a n d\ c

If : a^2+b^2+c^2-a b-b c-c a=0 , prove that a=b=c

Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=(a-b)^2+(b-c)^2+(c-a)^2

Given that a ,b ,c are distinct real numbers such that expressions a x^2+b x+c ,b x^2+c x+aa n dc x^2+a x+b are always non-negative. Prove that the quantity (a^2+b^2+c^2)//(a b+b c+c a) can never lie inn (-oo,1) uu [4 , oo) .

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Prove that: 2a^2+2b^2+2c^2-2a b-2b c-2c a=[(a-b)^2+(b-c)^2+(c-a)^2]

Prove that b^2c^2+c^2a^2+a^2b^2gtabc(a+b+c) , where a,b,c gt 0 .

The value of determinant |[b c-a^2,a c-b^2,a b-c^2],[a c-b^2,a b-c^2,b c-a^2],[a b-c^2,b c-a^2,a c-b^2]| is a. always positive b. always negative c. always zero d. cannot say anything

Show that the determinant |a^2+b^2+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^c+c^2b c+c a+a bb c+c a+a bb c+c a+a b a^2+b^2+c^2| is always non-negative. When is the determinant zero?

If a^2+b^2+c^2=16 and a b+b c+c a=10 , find the value of a+b+c

RD SHARMA ENGLISH-ALGEBRAIC IDENTITIES-All Questions
  1. if a-b=6 , ab=20 . find a^3-b^3

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  2. Write the following in expanded form: (i)(9x+2y+z)^2 (ii) (3x+2y...

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  3. Prove that a^2+b^2+c^2-a b-b c-c a is always non-negative for all valu...

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  4. If a+b+c=9 and a b+b c+c a=40 , find a^2+b^2+c^2dot

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  5. Simplify : (i)(a+b+c)^2 (ii) (a+b+c)^2-(a-b-c)^2

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  6. If x^2+1/(x^2)=98 , find the value of x^3+1/x^3

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  7. Simplify the following: 7x^3+8y^3-(4x+3y)(16 x^2-12 x y+9y^2)

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  8. If a-b=6 and a b=20 , find the value of a^3-b^3

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  9. If a+b=10 and a b=21 , find the value of a^3+b^3

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  10. If 4x^2+y^2=40 and x y=6, find the value of 2x+ydot

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  11. If a+b=7 and a b=12 , find the value of (a^2-a b+b^2)

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  12. If x^2+1/(x^2)=83. find the value of x^3-1/x^3

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  13. If x+y+z=1,x y+y z+z x=-1 and x y z=-1, find the value of x^3+y^3+z^3d...

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  14. Find the following products: (i) (0. 9 x+0. 7 y)(0. 81 x^2-0. 63 x y+...

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  15. If a+b+c=15 and a^2+b^2+c^2=83 , find the value of a^3+b^3+c^3-3abc

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  16. Without actually calculating the cubes. Find the value of each of th...

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  17. If a+b+c=9 and a^2+b^2+c^2=35 , find the value of a^3+b^3+c^3-3a b c

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  18. If x-1/x=3+2sqrt(2) , find the value of x^3-1/(x^3)

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  19. If x+y=12 and x y=32 , find the value of x^2+y^2dot

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  20. If 3x+2y=12 and x y=6, find the value of 9x^2+4y^2

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