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Show that: abs(((b+c)^2,a^2,bc) , ((c+a...

Show that:
`abs(((b+c)^2,a^2,bc) , ((c+a)^2,b^2,ca) , ((a+b)^2,c^2,ab))=(a^2+b^2+c^2)(a+b+c)(b-c)(c-a)(a-b)`

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Show that abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) , ((c-x)^2,(c-y)^2, (c-z)^2)) = 2(a-b)(b-c)(c-a)(x-y)(y-z)(z-x)

Prove that: |[(b+c)^2,a^2,a^2],[b^2,(c+a)^2,b^2],[c^2,c^2,(a+b)^2]|=2a b c(a+b+c)^3

Prove that, abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2)) =4 a^2b^2c^2 .

Prove that, abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1)) =1+ a^2+b^2+c^2 .

|{:(a,b,c),(a^2,b^2,c^2),(b+c,c+a,a+b):}|=(a-b)(b-c)(c-a)(a+b+c)

Show that abs((a,b,c),(a+2x,b+2y,c+2z),(x,y,z)) =0

Show that |{:(a^(2)+1,ab,ac),(ab,b^(2)+1,bc),(ca,bc,c^(2)+1):}|=1+a^(2)+b^(2)+c^(2)

|{:(a^2,ab,ac),(ab,b^2,bc),(ca,bc,c^2):}|= ?

Prove that |a ,b+c, a^2,b, c+a, b^2,c, a+b, c^2|=-(a+b+c)xx(a-b)(b-c)(c- a)

|{:(a^2,a^2-(b-c)^2,bc),(b^2,b^2-(c-a)^2,ca),(c^2,c^2-(a-b)^2,ab):}|=(a-b)(b-c)(c-a)(a+b+c)(a^2+b^2+c^2)

PATHFINDER-DETERMINATES-QUESTION BANK
  1. Without expanding,show that abs((x+1,x+2,x+a),(x+2,x+3,x+b),(x+3,x+4,x...

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  2. Solve fox x: abs((x,3),(5,2x))=abs((x,-4),(5,3))

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  3. Evaluateabs((1,omega,omega^2),(omega^2,1,omega),(omega^2,omega,1)) wer...

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  4. Using determainant find the area of the triangle formed by joining the...

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  5. If x+y+z=0 then show that abs((1,1,1),(x,y,z),(x^3,y^3,z^3)) = 0.

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  6. Evaluate the following determinantabs((x+lamda,x,x),(x,x+lamda,x),(x,x...

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  7. Without expanding prove that,abs((1,ab,1/a+1/b),(1,bc,1/b+1/c),(1,ca,1...

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  8. Show that abs((a,b,c),(a-b,b-c,c-a),(b+c,c+a,a+b)) = a^3+b^3+c^3-3abc.

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  9. If a,b c(all positive)are the p th,q thand r th terms repectively of a...

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  10. If p+-a, q+- b, r+-c and abs((p,b,c),(a,q,c),(a,b,r)) = 0 show that p...

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  11. find the value of :- (101)^2

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  12. Given that x =-9 is a root of abs((x,3,7),(2,x,2),(7,6,x))= 0 .Find th...

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  13. Show that abs(((a-x)^2,(a-y)^2,(a-z)^2) , ((b-x)^2,(b-y)^2,(b-z)^2) ...

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  14. Find the ratio in which the line joining the pts (-3,4,8) and (5,-6,4)...

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  15. Show that: abs(((b+c)^2,a^2,bc) , ((c+a)^2,b^2,ca) , ((a+b)^2,c^2,ab)...

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  16. If A,B,C be the angles of a triangle, then prove that ,abs((-1,cosC,co...

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  17. int(sinx)/(1+cosx)dx= ?

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  18. If x,y,z are all distinct and if abs((x,x^2,1+x^3),(y,y^2,1+y^3),(z,z^...

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  19. Prove that,abs((a^2+1,ab,ac),(ab,b^2+1,bc),(ca,cb,c^2+1))=1+a^2+b^2+c^...

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  20. Prove that,abs((-a^2,ab,ac),(ba,-b^2,bc),(ca,cb,-c^2))=4a^2b^2c^2.

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