If x - y = 13 and xy = 28, then find x² + y².

Solution:

Given, x - y = 13 and xy = 28,

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

(x - y)² = x² - 2xy + y²

(13)² = x² + y² - (2 × 28)

169 = x² + y² - 56

169 + 56 = x² + y²

x² + y² = 225

✦ Try This: If p - q = 50 and pq = 20, then find p² + q².

Given, p - q = 50 and pq = 20,

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

(p - q)² = p² - 2pq + q²

(50)² = p² + q² - (2 × 20)

2500 = p² + q² - 40

2500 + 40 = p² + q²

p² + q² = 2540

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

NCERT Exemplar Class 8 Maths Chapter 7 Problem 110

If x - y = 13 and xy = 28, then find x² + y².

Summary:

If x - y = 13 and xy = 28, then x² + y² is 225

☛ Related Questions:

• If m - n = 16 and m² + n² = 400, then find mn
• If a² + b² = 74 and ab = 35, then find a + b
• Verify: (ab + bc) (ab - bc) + (bc + ca) (bc - ca) + (ca + ab) (ca - ab) = 0