**If p – q = 9 and pq = 36, evaluate**

##### (i) p + q

##### (ii) p^{2} – q^{2}.

**Answer :**

##### (i) We know that

**(p + q) ^{2} = p^{2} + q^{2} + 2pq**

It can be written as

(p + q)^{2} = p^{2} + q^{2} – 2pq + 4pq

(p + q)^{2} = (p – q)^{2} + 4pq

It is given that

p – q = 9 and pq = 36

Substituting the values

(p + q)^{2} = 9^{2} + 4 × 36

By further calculation

(p + q)^{2} = 81 + 144 = 225

So we get

p + q = ± √225 = ± 15

##### (ii) We know that

**p ^{2} – q^{2} = (p – q) (p + q)**

Substituting the values

p^{2} – q^{2} = 9 ×±15

p^{2} – q^{2} = ± 135

**More Solutions:**

- If x + y = 6 and x – y = 4, find
- If x – 3 = 1/x, find the value of x2 + 1/x2.
- If x + y = 8 and xy = 3 ¾, find the values of
- Find the value of 2 (x + y)2 + (x – y)2.
- If a – b = 3 and ab = 4, find a3 – b3.
- Find the value of 8a3 – 27b3.
- If x + 1/x = 4, find the values of
- If x – 1/x = 5, find the value of x4 + 1/x4.
- If x – 1/x = √5, find the values of
- If x + 1/x = 6, find