If a + b = 25 and a² + b² = 225, then find ab.

Solution:

Given, a + b = 25 and a² + b² = 225

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

(a + b)² = a² + b² + 2ab

(25)² = 225 + 2ab

625 - 225 = 2ab

400 = 2ab

ab = 400/2

ab = 200

✦ Try This: If p + q = 40 and p² + q² = 250, then find pq.

Given, p + q = 40 and p² + q² = 250

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

(p + q)² = p² + q² + 2pq

40² = 250 + 2pq

1600 = 250 + 2pq

pq = (1600 - 250) ÷ 2

pq = 675

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

NCERT Exemplar Class 8 Maths Chapter 7 Problem 109

If a + b = 25 and a² + b² = 225, then find ab.

Summary:

If a + b = 25 and a² + b² = 225, then ab is 200

☛ Related Questions:

• If x - y = 13 and xy = 28, then find x² + y²
• If m - n = 16 and m² + n² = 400, then find mn
• If a² + b² = 74 and ab = 35, then find a + b