Question

if p -q=9 and pq =36 evaluate...

i)) p+q ii) p^2 - q^2

plzz define each step clearly

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

Answer 2

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