Problem And Solution SEAMO 2017 Paper E

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19. It is known that \(α. β\) are two roots of \(x^2+mx+n=0, α >1, -1<β<1.\) Find the value of \(m\) and \(n\) when \(α^3 + β^3≥4\).

(A) −1, −1
(B) 0, −1
(C) −1, 0
(D) 1, 1
(E) None of the above

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Solution

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20. Find the value of \(N\) in

\(\frac{1}{2!15!} + \frac{1}{3!14!} + \frac{1}{4!13!}+\frac{1}{5!12!}=\frac{N}{1!16!}\)

(A) 540
(B) 550
(C) 552
(D) 554
(E) 556

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Solution

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21. Given that

\(\log_8 a + \log_4 b^2 = 3\) and \(\log_8 b + \log_4 a^2 = 5\).

Find the value of \(ab\)

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Solution

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22. It is known that in \(Δ ABC\)

\(\frac{1}{\tan{\frac{A}{2}}} + \frac{1}{\tan{\frac{C}{2}}} = \frac{4}{\tan{\frac{B}{2}}}\)

if \(b=8\), find the value of \((a+c)\)

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Solution

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23. It is given that \(\overline{abcde}, a, \overline{bc}\) and \(\overline{de}\)  are square numbers. Let \(n\) represent the number of square numbers from \(\overline{abcde}\). Find the value of \(n\).

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Solution

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24. Find the largest positive integer \(N\) such that \(2^{50} + 4^{1015} + 16^N\) is a square number.

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Solution

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25. In \(ΔABC, \tan ∠CAB =\frac{22}{7}\)
The perpendicular \(AD\) divides \(BC\) at \(D\), such that \(BD = 3\) and \(DC = 17\). Find the area of \(ΔABC\)

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Solution

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Baca juga:
SEAMO PAPER E 2020
SEAMO PAPER E 2019
SEAMO PAPER E 2021