For the following questions answer them individually
If $$x^{2} -7x + 1 = 0$$, then what is the value of $$x + \frac{1}{x}$$?
If $$x^{2}- 2\sqrt{10}x+ 1 = 0$$, then what is the value of $$x - \frac{1}{x}$$?
If $$\ \frac{3x-1}{x}+\frac{5y-1}{y}+\frac{7z-1}{z}$$= 0, then what is the value of $$\ \frac{1}{x}+\frac{1}{y}+\frac{1}{z}\ $$?
If $$\ x^{2}\ - 3x + 1 = 0$$, then what is the value of $$\ x^{4}\ $$+Â $$\ \frac{1}{x^{4}}$$?
What is the value of $$\ \frac{(a^{2}+b^{2})(a-b)-(a-b)^{2}}{a^{2}b-ab^{2}}$$?
In the given figure, O is the center of the circle, $$\ \angle$$PQR = 100$$^\circ\ $$and $$\angle$$STR = 105$$^\circ$$. What is the value (in degrees) of $$\ \angle$$OSP?
In the given figure, EF = CE = CA, What is the value (in degrees) of $$\angle$$EAC?
If length of each side of a rhombus ABCD is 16 cm and ∠ABC = 120$$^\circ$$, then what is the length (in cm) of BD?
In an isosceles triangle PQR, ∠P = 130$$^\circ$$. If I is the in-centre of the triangle, then what is the value (in degrees) of ∠QIR?
In the given figure, O is the centre of a circle of radius 13 cm and AB is a chord perpendicular to OD. if CD = 8 cm, then what is the length (in cm) of AB?