Home
Class 12
MATHS
Using properties of determinants, show t...

Using properties of determinants, show that: `|[[(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`.

Answer

Step by step text solution for Using properties of determinants, show that: |[[(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. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION I) (Multiple Choice Questions)|6 Videos
  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (MOST IMPORTANT QUESTIONS FOR PRACTICE) (SECTION II) (SHORT ANSWER TYPE QUESTIONS )|11 Videos
  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (SECTION V) |9 Videos
  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARDS QUESTIONS FOR PRACTICE (MULTIPLE CHOICE QUESTIONS)|94 Videos
  • DIFFERENTIAL EQUATIONS

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEARS BOARD.S QUESTIONS FOR PRACTICE|50 Videos

Similar Questions

Explore conceptually related problems

Using the properties of determinant, show that : |[1,a+b,a^2+b^2],[1,b+c,b^2+c^2],[1,c+a,c^2+a^2]| = (a-b)(b-c)(c-a)

By using properties of determinants, show that : |[1,a,a^2],[1,b,b^2],[1,c,c^2]| = (a-b)(b-c)(c-a)

Using the properties of determinants show that : |[[1, a^2+bc, a^3],[1,b^2+ac,b^3],[1,c^2+ab,c^3]]|=(a-b)(b-c)(c-a)(a^2+b^2+c^2)

Using the properties of determinants show that : |[[-bc,b^2+bc,c^2+bc],[a^2+ac,-ac,c^2+ac],[a^2+ab,b^2+ab,-ab]]|=(ab+bc+ca)^3

Using the properties of determinants show that : |[[a^2, b^2, c^2],[bc,ca,ab],[a,b,c]]|=(a-b)(b-c)(c-a)(ab+bc+ca)

Using the properties of determinant, show that : |[a^2+1,ab,ac],[ab,b^2+1,bc],[ac,bc,c^2+1]| = 1+a^2+b^2+c^2

Using properties of determinant , show that : |{:(a,b,c),(a^(2),b^(2),c^(2)),( bc,ca,ab):}|=(ab+bc+ca)(a-b)(b-c)(c-a)

By using properties of determinants, show that |(a-b-c,2a,2a),(2b,b-c-a,2b),(2c,2c,c-a-b)|=(a+b+c)^3

Using the properties of determinants show that : |[[1,1,1],[a^2,b^2,c^2],[a^3,b^3,c^3]]|=(a-b)(b-c)(c-a)(ab+bc+ca) .

Use properties of determinants ot evaluate: {:|(2,a,abc),(2,b,bca),(2,c,cab)|