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In △ ABC, AB = AC. A circle drawn through B touches AC at D and intersect AB at P. If D is the midpoint of AC and AP = 2.5 cm, then AB is equal to:

If x² – 10x + 20 = 0, then find the value of (x – 3)² + 1/(x – 3)²

If (a + b) = 1 and (1/a) – 2b = 5/a then find the value of a² + b².

If x ²  – 15x + 51 = 0, then determine the value of (x – 5) + {1/(x – 5)}.

If (a + b) = 7 and ab = 10, then find the value of (a ²  + b ² ).

Determine the remainder when the polynomial 4x ³  - 5x ²  + 2x + 1 is divided by (4x - 3).

What is the HCF of (x³ + 3x² - x - 3) and (x³ + 4x² + x - 6)?