Question

if p - q= 9 and pq = 36, evaluate
P +q​

Answer 1

Given:

p-q=9                  

pq=36

i)) given p-q=9

     (p-q)²=9²               (squaring both sides LHS and RHS)

     p²+q²-2pq = 81     

     p²+q²-2×36=81     (substituting value of pq)

     p²+q²-72=81         (shifting -72 from LHS to RHS) 

     p²+q²=153..................................(1)

Now consider the equation

(p+q)²=p²+q²+2pq

(p+q)²=153+(2×36)    (substituting p²+q² from (1)  and pq(given))

(p+q)²=153+72=225

(p+q)²=225

Taking square root on both sides:

√(p+q)²=√225                                ((root of a square no),is the no itself)

   p+q=15 

ii)) now considering p²-q²

p²-q²=(p-q)×(p+q)         (algebraic formula)

p²-q²=(9)×(15)      (p-q=given     :   p+q=found from 1st answer)

p²-q²=135