For what value of k, the system of equations x-ky = 2 and 3x+2y = -5 has a unique solution?

The value of × satisfying the equations 1/x + 1/y = 8, 1/y+1/z = 12, 1/z +1/x = 10 is

If a, b, c, d, e and f satisfy 2a = 3b = 6c = 9d = 12e = 18f, then what is the value of (a + b)/(c + d + e + f)?

If x^3 – y^3 = 117/8 and x – y = 3/2 then the value of x^2 + xy + y^2 will be

If x + 1/x = k and x² + 1/x² = k, then values of k are

For what values of m, is mx² + mx + x8 + 9 a perfect square?