Subtract:`3a(a+b+c)-2b(a-b+c)` from`4c(-a+b+c)`

The roots of the quadratic equation (a + b-2c)x^2+ (2a-b-c) x + (a-2b + c) = 0 are

|(a-b-c, 2a, 2a),(2b, b-c-a,2b),(2c,2c,c-a-b)| = (a + b + c)^(3) .

Verify that a-: (b+c) ne ( a-: b) + ( a-: c) for each of the following values of a , b and c. : a=12,b=-4,c=2 .

Using the property of determinants prove that {:|( 3a,-a+b,-a+c),( -b+a, 3b,-b+c) ,( -c+a,-c+b,3c) |:} = 3( a+b+c) ( ab+bc+ca)

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

The expression ((a+b+c)(b+c-a)(c+a-b)(a+b-c))/(4b^2 c^2) for a triangle ABC is equal to

If a, b, c are positive real numbers such that a + b + c = 1 , then prove that a/(b + c)+b/(c+a) + c/(a+b) >= 3/2

Find the value of a,b,c and d from the equation: [(a-b,2a +c),(2a-b, 3c+d)]=[(-1,5),(0,13)]

Show that If a(b-c) x^2 + b(c-a) xy + c(a-b) y^2 = 0 is a perfect square, then the quantities a, b, c are in harmonic progresiion

|(a,b,c),(b,c,a),(c,a,b)| =