|{:((b+c)^2," "a^2," "a^2),(" "b^2,(c+...

`|{:((b+c)^2," "a^2," "a^2),(" "b^2,(c+a)^2," "b^2),(" "c^2," "c^2,(a+b)^2):}|=2abc(a+b+c)^3`

Topper's Solved these Questions

DETERMINANT
CHHAYA PUBLICATION|Exercise EXERCISE 2C|37 Videos
DETERMINANT
CHHAYA PUBLICATION|Exercise Sample Questions for Competitive Examination (Multiple Correct Answers Type)|5 Videos
DETERMINANT
CHHAYA PUBLICATION|Exercise EXERCISE 2A|36 Videos
DEFINITE INTEGRAL AS AN AREA
CHHAYA PUBLICATION|Exercise Assertion-Reason Type|2 Videos
DIFFERENTIAL EQUATIONS OF THE FIRST ORDER AND FIRST DEGREE
CHHAYA PUBLICATION|Exercise E ASSERTION-REASON TYPE|2 Videos

Similar Questions

Explore conceptually related problems

Using properties of determinants , prove that, |{:(a,b,c),(b,c,a),(c,a,b):}|=-(a^3+b^3+c^3-3abc) and hence show that, |{:(2bc-a^2," "c^2," "b^2),(" "c^2,2ca-b^2," "a^2),(" "b^2," "a^2,2ab-c^2):}|=(a^3+b^3+c^3-3abc)^2

Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}| , hence show that . |{:(0,c,b),(c,0,a),(b,a,0):}|^2=|{:(b^2+c^2," "ab," "ac),(" "ab,c^2+a^2," "bc),(" "ca," "bc,a^2+b^2):}|=4a^2b^2c^2

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

|{:(a+b+2c," "a," "b),(" "c,b+c+2a," "b),(" "c," "a,c+a+2b):}|=2(a+b+c)^3

Prove that, |{:((b+c)^(2),c^(2),b^(2)),(c^(2),(c+a)^(2),a^(2)),(b^(2),a^(2),(a+b)^(2)):}|=2(bc+ca+ab)^(3)

|{:(-a(b^2+c^2-a^2)," "2b^3," "2c^3),(" "2a^3,-b(c^2+a^2-b^2)," "2c^3),(" "2a^3," "2b^3,-c(a^2+b^2-c^2)):}|=abc(a^2+b^2+c^2)^3

Show that , |{:((a^2+b^2)/c," "c," "c),(" "a,(b^2+c^2)/a," "a),(" "b," "b,(c^2+a^2)/b):}|=4abc

|{:(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)

|{:(a,b,c),(a^2,b^2,c^2),(a^3,b^3,c^3):}|=abc(a-b)(b-c)(c-a)

prove that, |{:(" "2a,a-b-c," "2a),(" "2b," "2b,b-c-a),(c-a-b," "2c," "2c):}|=(a+b+c)^3

CHHAYA PUBLICATION-DETERMINANT -EXERCISE 2B

show that x =2 is a root to the equation |{:(x,-6,-1),(2,-3x,x-3),(-...
Text Solution
|
|{:(" "1+a^2-b^2," "2ab," "-2b),(" "2ab,1-a^2+b^2," ...
Text Solution
|
|{:((b+c)^2," "a^2," "a^2),(" "b^2,(c+a)^2," "b^2),(" "c^2," "c^2,(...
Text Solution
|
Factorise : |{:(x,y,z),(x^2,y^2,z^2),(yz,zx,xy):}|
Text Solution
|
|{:(b+c,a,b),(c+a,c,a),(a+b,b,c):}|
Text Solution
|
If |{:(x,x^2,x^3+1),(y,y^2,y^3+1),(z,z^2,z^3+1):}|=a and x ney nez , p...
Text Solution
|
Evaluate |{:(0,c,b),(c,0,a),(b,a,0):}|, hence show that . |{:(0,c,b)...
Text Solution
|
Express the square of |{:(a1,b1,0),(a2,b2,0),(a3,b3,0):}| as a third o...
Text Solution
|
prove that |{:(a,b,0),(0,a,b),(b,0,a):}|=a^3+b^3 , hence , find the va...
Text Solution
|
Prove that , the value of the determinant |{:(x+1,x+2,x+4),(x+3,x+5,...
Text Solution
|
|{:(b+c,a-c,a-b),(b-c,c+a,b-a),(c-b,c-a,a+b):}|=8abc
Text Solution
|
|{:(" "a^2," "bc,c^2+ca),(a^2+ab," "b^2," "ca),(" "ab,b^2+bc," "c^2...
Text Solution
|
|{:(2costheta,1,0),(1,2costheta,1),(0,1,2costheta):}|=(sin4theta)/(sin...
Text Solution
|
|{:(a,b,ax+by),(b,c,bx+cy),(ax+by,bx+cy,0):}|=(b^2-ac)(ax^2+2bxy+cy^2)
Text Solution
|
|{:(3x^2,3x,1),(x^2+2x,2x+1,1),(2x+1,x+2,1):}|=(x-1)^3
Text Solution
|
|{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...
Text Solution
|
|{:(1,1,1),(""^(n)c1,""^(n+1)c1,""^(n+2)c1),(""^(n+1)c2,""^(n+2)c2,""^...
Text Solution
|
|{:(x+y+z," "-z," "-y),(" "-z,x+y+z," "-x),(" "-y," "-x...
Text Solution
|
|{:(cos(x+y),sin(x+y),-cos(x+y)),(sin(x-y),cos(x-y),sin(x-y)),(sin2x,0...
Text Solution
|
prove that, |{:(0,cosalpha,-sinalpha),(sinalpha,0,cosalpha),(cosalpha,...
Text Solution
|