Question

6. The sum of the roots of a quadratic equation is 7 and the sum of their
cubes is 133. To find the quadratic equation, fill in the empty boxes.
Solution
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Answer 1

Step-by-step explanation:

$a + b = 7 \\ {a}^{3} + {b}^{3} = 133\\ (a + b)( {a}^{2} + {b}^{2} + ab) = 133 \\ (a + b)( {a}^{2} + {b}^{2} + 2ab - ab) = 133 \\ 7 \times ((a + b) {}^{2} - ab) = 133 \\ 7 \times (49 - ab) = 133 \\ 49 \times 7 - 7ab = 133 \\ 343 - 7ab = 133 \\ - 7ab = 133 - 343 \\ - 7ab = - 210 \\ ab = \frac{210}{7} \\ ab = 30 \\ quadartic \: equation \\ {x}^{2} - (a + b)x + ab = 0 \\ {x}^{2} - 7x + 30 = 0 \: \: answer$