PQR is an equilateral triangle whose side is 10 cm. What is the value (in cm) of the inradius of triangle PQR?

If 2x + 3y – 5z = 18, 3x + 2y + z = 29 and x + y + 3z = 17, then what is the value of xy + yz + zx?

Cost of 8 pencils, 5 pens and 3 erasers is Rs 111. Cost of 9 pencils, 6 pens and 5 erasers is Rs 130. Cost of 16 pencils, 11 pens and 3 erasers is Rs 221. What is the cost (in Rs) of 39 pencils, 26 pens and 13 erasers?

If x3 – 4x2 + 19 = 6(x – 1), then what is the value of [x2 + (1/x – 4)]?

If a + b + c = 9, ab + bc + ca = 26, a3 + b3 = 91, b3 + c3 = 72 and c3 + a3 = 35, then what is the value of abc?

α and β are the roots of the quadratic equation x2 – x – 1 = 0. What is the value of α8 + β8?

If A and B are the roots of the equation Ax2 – A2x + AB = 0, then what is the value of A and B respectively?

If x2 – 16x – 59 = 0, then what is the value of (x – 6)2 + [1/(x – 6)2]?