Question

find a^3-b^3 if a-b=12 and a×b=7​

Answer 1

Answer:

1980

Step-by-step explanation:

a³ - b³ = (a - b)(a² + b² + ab)___________________eq.1

As we know,

( a - b )² = a² + b² - 2ab

Therefore,

a² + b² = ( a - b )² + 2ab

Substituting the value of a² + b² in eq.1 , we get,

⇒ a³ - b³ = (a - b) [( a - b )² + 2ab + ab]

Substituting the value of a-b and ab from the question, we get,

⇒ a³ - b³ = 12 × [(12)² + 2 × 7 + 7]

⇒ a³ - b³ - 12 × ( 144 + 14 + 7 )

⇒ a³ - b³ = 12 × 165

⇒ a³ - b³ = 1980

Answer 2

Answer:

Step-by-step explanation:

Since ,

$(a-b)^2=a^2+b^2+2ab\\Therfore\\12^2=a^2+b^2+2ab\\Therefore\\144=a^2+b^2+2(7)=a^2+b^2+14Therefore\\130=a^2+b^2\\Since\\a^3-b^3=(a-b)(a^2+b^2+ab)\\\\since \\a-b=7, a^2+b^2=130 , ab=7\\Therefore\\a^3-b^3=(12)(130+7) \\Therefore,\\a^3-b^3=12*137=1644-ANS$

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