1.

If \(a + b = \frac 7 3\) and \(a^2 + b^2 = \frac {31} 9,\) find 27 (a3 + b3).1. 1542. 1563. 1524. 164

Answer» Correct Answer - Option 1 : 154

Given:

a + b = 7/3

a2 + b2 = 31/9

Formula used:

(a + b)2 = a2 + b2 + 2ab

a3 + b3 = (a + b)( a2 + b2 – ab)

Calculation:

According to the question,

⇒ a + b = 7/3

Squaring both sides,

⇒ (a + b)2 = (7/3)2

⇒ a2 + b2 + 2ab = 49/9

⇒ 31/9 + 2ab = 49/9

⇒ 2ab = 49/9 – 31/9

⇒ 2ab = 18/9

⇒ 2ab = 2

⇒ ab = 1

According to the formula,

⇒ a3 + b3 = (a + b)( a2 + b2 – ab)

Multiply 27 on both sides,

⇒ 27(a3 + b3) = 27(a + b)( a2 + b2 – ab)

⇒ 27(a3 + b3) = 27(7/3)( 31/9 – 1)

⇒ 27(a3 + b3) = 27(7/3)( 22/9)

⇒ 27(a3 + b3) = 22 × 7

⇒ 27(a3 + b3) = 154

∴ The value of 27(a3 + b3) is 154.


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