Express `(1 + a^2)(1 + b^2)(1+c^2)` as the sum of two squares.

Express (1+a^2)(1+b^2) as the sum of two squares.

Express the matrix [3-2-4 3-2-5-1 1 2] as the sum of a symmetric and skew-symmetric matrix.

The sum of the squares of the first n positive integers 1^2 + 2^2 + 3^2 + ………+ n^2 is (n(n +1)(2n+1))/(6) . What is the sum of the squares of the first 9 positive integers?

Integers a, b, c satisfy a + b - c = 1 and a^2 + b^2 - c^2 = -1 . What is the sum of all possible values of a^(2) + b^(2) + c^(2) ?

If the sum of first n terms of an A P is c n^2, then the sum of squares of these n terms is (2009) (n(4n^2-1)c^2)/6 (b) (n(4n^2+1)c^2)/3 (n(4n^2-1)c^2)/3 (d) (n(4n^2+1)c^2)/6

If the sum of the roots of x^(2) + bx + 1 = 0 , is equal to the sum of their squares, then b =

Show that the points A (5,6) B (1,5) and C (2,1) and D (6,2) are the vertices of a square ABCD.

Express the matrix B= [{:(,2,-2,),(,-1,3,):}] as the sum of a symmetric and a skew symmetric matrix.

If the sum of the coefficients in the expansion of (b + c)^(20) {1 +(a -2) x}^(20) is equal to square of the sum of the coefficients in the expansion of [2 bcx - (b + c)y]^(10) , where a, b, c are positive constants, then

Show that the points A(5,\ 6),\ \ B(1,\ 5),\ \ C(2,\ 1) and D(6,\ 2) are the vertices of a square.