help my inner mathematician to grow

For the quadratic equation to have equal roots.

b² - 4ac = 0         ...............(1)

In our quadratic equation, (P-Q)²x²+2(P²-Q²)x+k = 0

a = (P-Q)²

b = 2(P²-Q²)

c = k

Substituting the values in eqn (1), we get

(2(P²-Q²))² = 4 (P-Q)² . k

4 ((P-Q)(P+Q))² = 4k (P-Q)² 

⇒ k = ( P + Q)² or P² + Q² + 2PQ