If $\displaystyle pq$ = 4, and $\displaystyle p^2q + pq^2 +p + q$= 60, then $\displaystyle p+q$ equals?? a 9 b 10 c 12 d 15 e 20
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Hello, Originally Posted by foreverbrokenpromises If $\displaystyle pq$ = 4, and $\displaystyle p^2q + pq^2 +p + q$= 60, then $\displaystyle p+q$ equals?? a 9 b 10 c 12 d 15 e 20 $\displaystyle p^2q+pq^2=pq(p+q)$ Hence we have $\displaystyle (p+q)(pq+1)=60$ Finish it
Originally Posted by foreverbrokenpromises If $\displaystyle pq$ = 4, and $\displaystyle p^2q + pq^2 +p + q$= 60, then $\displaystyle p+q$ equals?? a 9 b 10 c 12 d 15 e 20 $\displaystyle p^2q + pq^2 +p + q= 60 \implies pq(p+q) +(p + q)= 60$ $\displaystyle \implies (pq+1)(p+q) = 60 \implies 5 (p+q) = 60 \implies \text{c}$
ANOTHER WAY: Solve for p $\displaystyle p=\frac{4}{q}$ then substitute this $\displaystyle \frac{4}{q}$ into the equation $\displaystyle (\frac{4}{q})^2q+\frac{4}{q}q^2+\frac{4}{q}+q=60$ solve for q, reapeat the process with p, and then add 'em up!
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