Prove that : |{:((y+z)^(2),x^(2),x^(2)),...

Prove that : `|{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2),z^(2),(x+y)^(2)):}|=2xyz (x+y+z)^(3)`

Topper's Solved these Questions

DETERMINANTS
MODERN PUBLICATION|Exercise Exercise 4(c ) (SHORT ANSWER TYPE QUESTIONS)|4 Videos
DETERMINANTS
MODERN PUBLICATION|Exercise Exercise 4(d) (SHORT ANSWER TYPE QUESTIONS)|4 Videos
DETERMINANTS
MODERN PUBLICATION|Exercise Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (I))|19 Videos
CONTINUITY AND DIFFERENTIABILITY
MODERN PUBLICATION|Exercise CHAPTER TEST|12 Videos
DIFFERENTIAL EQUATIONS
MODERN PUBLICATION|Exercise CHAPTER TEST (9)|12 Videos

Similar Questions

Explore conceptually related problems

Prove that |{:(x^(2),,x^(2)-(y-z)^(2),,yz),(y^(2),,y^(2)-(z-x)^(2),,zx),(z^(2),,z^(2)-(x-y)^(2),,xy):}| =(x-y) (y-z) (z-x)(x+y+z) (x^(2)+y^(2)+z^(2))

Using properties of determinants, prove that : |{:((x+y)^(2),zx,xy),(zx,(z+y)^(2),xy),(zy,xy,(z+x)^(2)):}|=2xyz(x+y+z)^(3) .

Prove that : =2|{:(1,1,1),(x,y,rz),(x^(2),y^(2),z^(2)):}|=(x-y)(y-z)(z-x)

prove that: |(y^(2)z^(2),yz,y+z),(z^(2)x^(2),zx,z+x),(x^(2)y^(2),xy,x+y)|=0

Prove the following : |{:(x,y,z),(x^(2),y^(2),z^(2)),(x^(3),y^(3),z^(3)):}|=|{:(x,x^(2),x^(3)),(y,y^(2),y^(3)),(z,z^(2),z^(3)):}|=xyz(x-y)(y-z)(z-x)

The value of (x^(2)-(y-z)^(2))/((x+z)^(2)-y^(2))+(y^(2)-(x-z)^(2))/((x+y)^(2)-z^(2))+(z^(2)-(x-y)^(2))/((y+z)^(2)-x^(2)) is -1(b)0(c)1(d) None of these

The value of (x^(2)-(y-z)^(2))/((x+z)^(2)-y^(2))+(y^(2)-(x-z)^(2))/((x+y)^(2)-z^(2))+(z^(2)-(x-y)^(2))/((y+z)^(2)-x^(2))

Prove that : |{:(x-y-z,2x,2x),(2y,y-z-x,2y),(2z,2z,z-x-y):}|

Prove that : |{:(y+z,x,y),(z+x,z,x),(x+y,y,z):}|=(x+y+z)(x-z)^(2)

MODERN PUBLICATION-DETERMINANTS-Exercise 4(b) (LONG ANSWER TYPE QUESTIONS (II))

For any scalar p prove that =|xx^2 1+p x^3y y^2 1+p y^3z z^2 1+p z^3|=...
Text Solution
|
|(x+y+z,-z,-y),(-z,x+y+z,-x),(-y,-x,x+y+z)|=2(x+y)(y+z)(z+x)
Text Solution
|
Prove: |2y y-z-x2y2z2z z-x-y x-y-z2x2x|=(x+y+z)^3
Text Solution
|
|(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|
Text Solution
|
Show that: |3a-a+b-a+c-b+a3b-b+c-c+a-c+b3c|=3(a+b+c)(a b+b c+c a)dot
Text Solution
|
Using properties of determinants. Find the value of 'x' |(4-x,4+x,4+...
Text Solution
|
Solve: |a+x a-x a-x a-x a+x a-x a-x a-x a+x|=0
Text Solution
|
Prove that |[x, sintheta, costheta],[-sintheta, -x, 1],[costheta, 1, ...
Text Solution
|
Prove that |{:(1+a,1,1),(1,1+b,1),(1,1,1+c):}| =abc (1+(1)/(a)+(1)/...
Text Solution
|
Prove that : |{:((y+z)^(2),x^(2),x^(2)),(y^(2),(x+z)^(2),y^(2)),(z^(2)...
Text Solution
|
Prove that | ((b+c)^2, a^2,a^2),(b^2,(c+a)^2,b^2),(c^2,c^2,(a+b)^2)|=2...
Text Solution
|
|[(b+c)^2,ab,ca],[ab,(a+c)^2,bc],[ac,bc,(a+b)^2]|=2abc(a+b+c)^3
Text Solution
|
Show that Delta=|(y+z)^2x y z xx y(x+z)^2y z x z y z(x+y)^2|=2x y z(x+...
Text Solution
|
If a, b, c are positive and unequal, show that value of the determinan...
Text Solution
|
Using properties of determinants, prove that |a a+b a+b+c2a3a+2b4a...
Text Solution
|
Using properties of determinants. Prove that |1 1+p1+p+q2 3+2p4+3p+2q3...
Text Solution
|
Q. |(x+y,x,x),(15x+4y,4x,2x),(10x +8y,8x,3x)|=x^3
Text Solution
|
Prove |[-bc, b^2+bc, c^2+bc] , [a^2+ac, -ac, c^2+ac] , [a^2+ab, b^2+ab...
Text Solution
|
Prove that |{:(a^(2), a^(2)-(b-c)^(2), bc), (b^(2), b^(2)-(c-a)^(2), ...
Text Solution
|
If p, q, r are not in G.P. and |[1,q/p,alpha+q/p],[1,r/p,alpha+r/q],[p...
Text Solution
|