If p – q = 9 and pq = 36, evaluate

If p – q = 9 and pq = 36, evaluate

(i) p + q

(ii) p² – q².

Answer :

(i) We know that

(p + q)² = p² + q² + 2pq

It can be written as

(p + q)² = p² + q² – 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 = 9² + 4 × 36

By further calculation

(p + q)² = 81 + 144 = 225

So we get

p + q = ± √225 = ± 15

(ii) We know that

p² – q² = (p – q) (p + q)

Substituting the values

p² – q² = 9 ×±15

p² – q² = ± 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