If a+b=7 & a^2+b^2=11 then find a^3+b^3?
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Solution :
a + b = 7 ----( 1 )
a² + b² = 11----( 2 )
a² + b² + 2ab = (a + b )²
=> 11 + 2ab = 7²
=> 2ab = 49 - 11
=> ab = 38/2
=> ab = 19 -----( 3 )
Now ,
a³ + b³ = ( a + b )³ - 3ab(a+b)
= 7³ - 3 × 19 × 7
= 343 - 399
= - 56
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