Question

a+b=7 and ab=3 value a3+b3

Answer 1

Answer:

280

Step-by-step explanation:

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Answer 2

$\large\underline{\sf{Given- }}$

$\red{\rm :\longmapsto\:a + b = 7}$

and

$\red{\rm :\longmapsto\:ab = 3}$

$\large\underline{\sf{To\:Find - }}$

$\red{\rm :\longmapsto\: {a}^{3} + {b}^{3} }$

$\green{\large\underline{\sf{Solution-}}}$

Given that,

$\red{\rm :\longmapsto\:a + b = 7}$

and

$\red{\rm :\longmapsto\:ab = 3}$

Consider,

$\red{\rm :\longmapsto\: {a}^{3} + {b}^{3} }$

$\rm \: = \: {(a + b)}^{3} - 3ab(a + b)$

$\rm \: = \: {(7)}^{3} - 3(3)(7)$

$\rm \: = \: 343 - 63$

$\rm \: = \: 280$

Hence,

$\red{\rm \implies\:\boxed{ \tt{ \: {a}^{3} + {b}^{3} = 280 \: }}}$

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Explore more :-

More Identities to know :-

(a + b)² = a² + 2ab + b²

(a - b)² = a² - 2ab + b²

a² - b² = (a + b)(a - b)

(a + b)² = (a - b)² + 4ab

(a - b)² = (a + b)² - 4ab

(a + b)² + (a - b)² = 2(a² + b²)

(a + b)³ = a³ + b³ + 3ab(a + b)

(a - b)³ = a³ - b³ - 3ab(a - b)