Solve it

Algebra Level 2

If p + q + 1 = 0 p+q+1=0 , then what is the value of p 2 + q 2 + 1 p + q + p q \frac{p^2 +q^2 +1}{p+q+pq}

8-p 1 8-q -2 -1 2

Gaurav Purswani by Gaurav Purswani , 29, USA

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

Pranjal Jain
Jan 13, 2015

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

Squaring both sides, 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 p^2+q^2 and p + q p+q in required expression,

p 2 + q 2 + 1 p + q + p q = 2 − 2 p q − 1 + p q = − 2 \dfrac{p^2+q^2+1}{p+q+pq}\\=\dfrac{2-2pq}{-1+pq}\\=\boxed{-2}

1 Helpful 0 Interesting 0 Brilliant 0 Confused

@Gaurav Purswani, I have edited some L a T e X LaTeX in your solution. Please check it once for accuracy. You can also use it for future referencing.

Pranjal Jain - 6 years, 5 months ago

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...