Question

If a + b + c = 9 and ab + bc + ac = 40, then find the value for : a^2 + b^2 + c^2

Answer 1

$\large\bf\underline \blue {To \: \mathscr{f}ind:-}$

• we need to find the value of a² + b² + c²

$\huge\bf\underline \purple{ \mathcal{S}olution:-}$

$\bf\underline{\red{Given:-}}$

• a + b + c = 9
• ab + bc + ac = 40

we know that,

(a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca

↛ a² + b² + c² = (a + b + c)² - 2(ab + bc + ca)

• putting values of (a + b + c) and (ab + bc + ca)

↛ a² + b² + c² = 9² - 2(40)

↛ a² + b² + c² = 81 - 80

↛ a² + b² + c² = 1

hence,

• Value of a² + b² + c² is 1

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✫Some Identities :-

» (a + b)² = a² + b² + 2ab

» (a - b)² = a² + b² - 2ab

» (a + b)(a - b) = a² - b²

» (a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ac

» a³ + b³ = (a + b)(a² + b² - ab)

» a³ - b³ = (a - b)(a² + b² + ab)

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Answer 2

Answer:

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Step-by-step explanation: