Question

If a + b + c = 9 and ab + bc + ca = 26 then a^2 + b^2 + c^2 = -----

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Answer 1

Given:-

• a + b + c = 9
• ab + bc + ca = 26

To find:-

• a² + b² + c²

Answer:-

Given that,

a + b + c = 9

On squaring both sides,

→ (a + b + c)² = (9)²

Expanding LHS using the identity,

(x + y + z)² = x² + y² + z² + 2(xy + yz + zx)

→ a² + b² + c² + 2(ab + bc + ca) = 81

Putting the values given in the question,

→ a² + b² + c² + 2(26) = 81

→ a² + b² + c² + 52 = 81

→ a² + b² + c² = 81 - 52

→ a² + b² + c² = 29 Ans

Extra knowledge:-

• (a + b)² = a² + b² + 2ab
• (a - b)² = a² + b² - 2ab
• a² - b² = (a + b)(a - b)
• (a + b)³ = a³ + b³ + 3ab(a + b)
• (a - b)³ = a³ - b³ - 3ab(a - b)
• a³ + b³ = (a + b)(a² + b² - ab)
• a³ - b³ = (a - b)(a² + b² + ab)
• (a + b + c)² = a² + b² + c² + 2(ab + bc + ca)
• a³ + b³ + c³ - 3abc = (a + b + c)(a² + b² + c² - ab - bc - ca)

Answer 2

Answer:

(a+b+c)^2=a^2 +b^2+c^2+2ab+2bc+2ac

(9)^2=a^2+b^2+c^2+2(ab+bc+ac)

81= a^2+b^2+c^2+2×26

a^2+b^2+c^2=81-52

=29