If p + q = 12 and pq = 22, then find p² + q².

Solution:

Given, p + q = 12 and pq = 22

Using standard identity: (a + b)² = a² + 2ab + b², we can write

(p + q)² = p² + 2pq + q²

(12)² = p² + q² + (2 × 22)

144 = p² + q² + 44

144 - 44 = p² + q²

p² + q² = 100

✦ Try This: If a - b = 15 and ab = 10, then find a² + b²

Given, a - b = 15 and ab = 10

Using standard identity : (a - b)² = a² - 2ab + b², we can write

(15)² = a² - 2(10) + b²

a² + b² = 225 + 20

a² + b² = 245

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 9

NCERT Exemplar Class 8 Maths Chapter 7 Problem 108

If p + q = 12 and pq = 22, then find p² + q².

Summary:

If p + q = 12 and pq = 22, then p² + q² is 100

☛ Related Questions:

• If a + b = 25 and a² + b² = 225, then find ab
• If x - y = 13 and xy = 28, then find x² + y²
• If m - n = 16 and m² + n² = 400, then find mn