EXPLANATION.
⇒ a + b = 7. - - - - - (1).
⇒ ab = 5. - - - - - (2).
As we know that,
Formula of :
⇒ (x³ + y³) = (x + y)(x² - xy + y²).
⇒ (x² + y²) = (x + y)² - 2xy.
Using this formula in this question, we get.
⇒ (a³ + b³) = (a + b)(a² - ab + b²).
⇒ (a³ + b³) = (a + b)[(a + b)² - 2ab - ab].
⇒ (a³ + b³) = (a + b)[(a + b)² - 3ab].
Put the values in the equation, we get.
⇒ (a³ + b³) = (7)[(7)² - 3(5)].
⇒ (a³ + b³) = (7)[49 - 15].
⇒ (a³ + b³) = (7)[34].
⇒ (a³ + b³) = 7 x 34.
⇒ (a³ + b³) = 238.
Option [D] is correct answer.
MORE INFORMATION.
(1) (x + y)² = x² + y² + 2xy.
(2) (x - y)² = x² + y² - 2xy.
(3) (x² - y²) = (x + y)(x - y).
(4) (x² + y²) = (x + y)² - 2xy.
(5) (x³ + y³) = (x + y)(x² - xy + y²).
(6) (x³ - y³) = (x - y)(x² + xy + y²).
(7) (x + y)³ = x³ + 3x²y + 3xy² + y³.
(8) (x - y)³ = x³ - 3x²y + 3xy² - y³.