An algebra problem by Gaurav Purswani

Algebra Level 2

IF P+Q+1=0 Then find the value of {(P^2 +Q^2+1)/P+Q+PQ}

8-P -2 1 8-Q 4

Gaurav Purswani by Gaurav Purswani , 29, USA

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1 solution

Omkar Kulkarni
Jan 14, 2015

p + q + 1 = 0 ⇒ p + q = − 1 p+q+1=0 \Rightarrow p+q=-1

( p + q ) 2 = ( − 1 ) 2 (p+q)^2 = (-1)^2

p 2 + q 2 + 2 p q = 1 ⇒ p 2 + q 2 = 1 − 2 p q p^2 + q^2 + 2pq = 1 \Rightarrow p^2 + q^2 = 1 - 2pq

Substituting,

p 2 + q 2 + 1 p + q + p q \frac {p^2 + q^2 + 1}{p + q + pq}

= 2 − 2 p q − 1 + p q = \frac {2-2pq}{-1+pq}

= − 2 = \boxed {-2}

4 Helpful 0 Interesting 0 Brilliant 0 Confused

good keep it up

Gaurav Purswani - 6 years, 4 months ago

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