" 29."b^(2)c^(3)+8bc^(4)+12c^(5)

if a , b , c and d are in proportion, prove that : (i) (a-b)/(c-d)= sqrt((3a^(2) + 8b^(2))/(3c^(2) + 8d^(2))) (ii) ((5a^(2) + 12c^(2))/(5b^(2) + 12d^(2))) = sqrt((3a^(4) - 7c^(4))/(3b^(4) - 7d^(4)))

Simplify : (2a+3b+4c) ( 4a^(2) + 9b^(2) + 16c^(2) -6ab - 12bc - 8ca )

If (a-2b-3c+4d)(a+2b+3c+4d) = (a+2b-3c-4d)(a-2b+3c-4d) then 2ad = "(a) 3bc (b) bc (c) 5bc (d) 2bc"

Find the product : (i) (a+2b+4c)(a^(2)+4b^(2)+16c^(2)-2ab-8bc-4ca) (ii) (3x-5y-4)(9x^(2)+25y^(2)+15xy+12x-20y+16) (iii) (2-3b-7c)(4+9b^(2)+49c^(2)+6b-21bc+14c) (iv) (sqrt(2)a+2sqrt(2)b+c)(2a^(2)+8b^(2)+c^(2)-4ab-2sqrt(2)bc-sqrt(2)ac)

Find the product : (i) (a+2b+4c)(a^(2)+4b^(2)+16c^(2)-2ab-8bc-4ca) (ii) (3x-5y-4)(9x^(2)+25y^(2)+15xy+12x-20y+16) (iii) (2-3b-7c)(4+9b^(2)+49c^(2)+6b-21bc+14c) (iv) (sqrt(2)a+2sqrt(2)b+c)(2a^(2)+8b^(2)+c^(2)-4ab-2sqrt(2)bc-sqrt(2)ac)

If A is a skew-symmetric matrix of order 2 and B, C are matrices [[1,4],[2,9]],[[9,-4],[-2,1]] respectively, then A^(3) (BC) + A^(5) (B^(2)C^(2)) + A^(7) (B^(3) C^(3)) + ... + A^(2n+1) (B^(n) C^(n)), is

If A is a skew-symmetric matrix of order 2 and B, C are matrices [[1,4],[2,9]],[[9,-4],[-2,1]] respectively, then A^(3) (BC) + A^(5) (B^(2)C^(2)) + A^(7) (B^(3) C^(3)) + ... + A^(2n+1) (B^(n) C^(n)), is

If ab + bc + ca = 8 and a+b+c = 12 then (a^(2) + b^(2) + c^(2)) is equal to :