Question

22. Express 15.353535.. into rational number *
(2 Points)
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23. If (x+3) is a factor of x2+mx-3, then find the value of m?*
(2 Points)
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24. If a+b =10 and ab=21, find the value of a3+b3 *
(2 Points)
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Answer 1

Answer:

22)

$let \: x = 15.3535......(1) \\ multiply \: 100 \: on \: bot \: sides \: of \: (1) \\ 100(x) = 100(15.3535...) \\ 100x = 1535.3535......(2) \\ subtracting \: (1) \: from \: (2) \\ 100x = 1535.3535... \\ \: \: \: \: \: \: \: - \: \: \: \: x = \: \: \: \: 15.3535... \: \: \: \: \: \\ 99x = 1520.00 \\ x = \frac{1520}{99}$

23) x+3 is factor of given p(x)

.°. x+3 = 0

.°. x = (-3)

substituing x = (-3) in p(x)

${x}^{2} + mx - 3 = 0\\ {(-3)}^{2} + m(-3) - 3 = 0$

9-3m-3 = 0

6-3m = 0

3m = 6

m= 2

24) a+b = 10

ab = 21

${(a + b)}^{3} = {a}^{3} + {b}^{3} + 3ab(a + b) \\ {(10)}^{3} = {a}^{3} + {b}^{3} + 3(21)(10) \\ 1000 = {a}^{3} + {b}^{3} + 630 \\ {a}^{3} + {b}^{3} = 1000 - 630 \\ {a}^{3} + {b}^{3} = 370 \\ Thus \: the \: value \: of \: {a}^{3} + {b}^{3} = 370$