Question

if p-q=9 and pq=36 find the value of p^2-q^2

Due date tomorrow please help- (╥﹏╥)​

Answer 1

Answer:

The answer will be 135.

Step-by-step explanation:

Given;

p-q = 9. (i)

pq = 36

Square equation (i) on both side;

(p-q)^2 = (9)^2;

p^2 + q^2 -2pq = 81;

p^2 + q^2 -2(36) = 81; (from eq.(ii))

p^2 + q^2 = 81 + 72;

p^2 + q^2 = 153;

Add 2pq on both side;

p^2 + q^2 + 2pq= 153 + 2pq;

(p+q)^2 = 153+ 2(36); (from eq. (ii))

(p+q)^2 = 225;

p + q = 15;

Now we've got two equations to find the value the two variables.

These are,

p-q = 9;

p+q = 15;

Add both the equations;

p-q + p+q = 9 + 15;

2p = 24;

p = 12.

Now, p + q = 15

12 + q = 15;

q = 3.

Hence, p^2 - q^2 = (12)^2 - (3)^2;

= 144 - 9

= 135.

That's all.