The HCF of two numbers is 145 and their LCM is 2175. If one number is 725, find the other.

Show that the x = -3 is a solution of x² + 6x + 9 = 0

If the points (2, 1) and (1,-2) are equidistant from the point (x, y), show that x + 3y = 0.

OR

If R (5, 6) is the midpoint of the line segment joining the points A (6, 5) and B (4, y) then find the value of ‘y’.

The line segment joining the midpoints of the adjacent sides of a quadrilateral form a ________ .

If tan²45° - cos²30° = x sin 45°cos 45° then x =?

OR

If A and B are acute angles such that sin A = cos B, prove that A + B = 90°.