If m - n = 16 and m² + n² = 400, then find mn.

Solution:

Given, m - n = 16 and m² + n² = 400,

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

(m - n)² = m² - 2mn + n²

(16)² = 400 - 2mn

256 = 400 - 2mn

2mn = 400 - 256

2mn = 144

mn = 144/2 = 72

✦ Try This: If x - y = 36 and x² + y² = 600 then find xy.

Given, x - y = 36 and x² + y² = 600,

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

(x - y)² =x² - 2xy + y²

(36)² = 600 - 2xy

1296 = 600 - 2xy

2xy = 600 - 1296

2xy = -696

xy = -696/2 = -348

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

NCERT Exemplar Class 8 Maths Chapter 7 Problem 111

If m - n = 16 and m² + n² = 400, then find mn.

Summary:

If m - n = 16 and m² + n² = 400, then mn is 72

☛ Related Questions:

• 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
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