exam Maths Puzzle Numerical Ability

If ABCD is a rectangle and P is any point in its interior, prove that:
(AP)(AP)+(PC)(PC)=(PB)(PB)+(PD)(PD)

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exam Other Question
Find the two solutions to this equation.
ax^2+8ax=0 solve homogeneous system of equations

x - 2y + 3z = 0
3x - 7y - 4z = 0
4x - 4y + z = 0

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