Grade 11Algebra

I wanted the solution of question 3 in the last 2 lines of the image

Anurag

9 Years agoGrade 11

Approved Tutor Answer9 Years ago

Note that $P(P(\alpha)) = P(\alpha) (P(\alpha)-1) +1$ so that we have

$\Rightarrow P(\alpha) (P(\alpha)-1) = P(P(\alpha) ) -1$

The product similarly simplifies to

$= (P(P(\alpha)) -1)P(P(\alpha)) P(P(P(\alpha)))$

$= (P(P(P(\alpha))) -1) P(P(P(\alpha)))$

$= P(P(P(P(\alpha))))-1$

$=\boxed{-1}$

since

$P(P(P(P(\alpha)))) = 0$

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