If a + b = 6 and ab = 8, find: a^3 + b^3.

Using the formula, [∵ (x \+ y) 3 = x 3 \+ y 3 \+ 3xy(x \+ y)] So, (a \+ b) 3 = a 3 \+ b 3 \+ 3ab(a \+ b) Putting the values a \+ b = 6 and ab = 8, we get ⇒ (6) 3 = a 3 \+ b 3 \+ 3 x 8 x 6 ⇒ 216 = a 3 \+ b 3 \+ 144 ⇒ a 3 \+ b 3 = 216 \- 144 ⇒ a 3 \+ b 3 = 72 Hence, the value of a 3 \+ b 3 is 72.

Mathematics

If a + b = 6 and ab = 8, find: a³ + b³.

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Using the formula,

[∵ (x + y)³ = x³ + y³ + 3xy(x + y)]

So,

(a + b)³ = a³ + b³ + 3ab(a + b)

Putting the values a + b = 6 and ab = 8, we get

⇒ (6)³ = a³ + b³ + 3 x 8 x 6

⇒ 216 = a³ + b³ + 144

⇒ a³ + b³ = 216 - 144

⇒ a³ + b³ = 72

Hence, the value of a³ + b³ is 72.

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Mathematics

If a + b = 6 and ab = 8, find: a³ + b³.

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