Question

( a + b )^2 = 189 and 6ab = 78 find the value of ( a^2 + b^2 )

Answer 1

Answer:

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Step-by-step explanation

Answer 2

Answer:

Step-by-step explanation:

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Given :

(a + b)² = 189,

6ab = 78,

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To  Find :

The value of :

3(a² + b²)

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We know that,

⇒ (a + b)² = a² + 2ab + b²

∴ a² + 2ab + b² = 189,...(i)

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We know that,

6ab = 78

⇒ ab =  \frac{78}{6}  

⇒ ab = 13 ....(ii)

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Substituting value of ab in (i),

We get,

⇒ a² + 2ab + b² = 189

⇒ a² + 2(13) + b² = 189

⇒ a² + 26 + b² = 189

⇒ a² + b² = 189 - 26

⇒ a² + b² = 163...(iii)

∴ 3 (a² + b²) = 3(163) = 489,.

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