Question

If a+b+c= 12 and a² + b² + c²=100, find the value of ab + bc + ca.
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Answer 1

Solution:

Given Information:

→ a + b + c = 12 — (i)

→ a² + b² + c² = 100 — (ii)

Squaring both sides of equation (i), we get:

→ (a + b + c)² = 12²

Using identity (a + b + c)² = a² + b² + c² + 2(ab + bc + ac), we get:

→ a² + b² + c² + 2(ab + bc + ac) = 144

Substituting the value of a² + b² + c², we get:

→ 100 + 2(ab + bc + ac) = 144

→ 2(ab + bc + ac) = 144 - 100

→ 2(ab + bc + ac) = 44

→ ab + bc + ac = 22

★ Therefore, the value of ab + bc + ac is 22.

Learn More:

Algebraic Identities.

• (a + b)² = a² + 2ab + b²
• (a - b)² = a² - 2ab + b²
• a² - b² = (a + b)(a - b)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ac)
• (a + b)³ = a³ + 3ab(a + b) + b³
• (a - b)³ = a³ - 3ab(a - b) - b³
• a³ + b³ = (a + b)(a² - ab + b²)
• a³ - b³ = (a - b)(a² + ab + b²)
• (x + a)(x + b) = x² + (a + b)x + ab
• (x + a)(x - b) = x² + (a - b)x - ab
• (x - a)(x + b) = x² - (a - b)x - ab
• (x - a)(x - b) = x² - (a + b)x + ab