#160; #160; #160;27a2 #160; #160;75b2= #160;39a2 #160; #160;25b2= #160;33a2 #160; #160;5b2= #160;33a #160;+ #160;5b3a #160; ...

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Ratio

27 a2-75 b2

Question

27a² $-$ 75b²

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Solution

$27 a^{2} - 75 b^{2} = 3 (9 a^{2} - 25 b^{2}) = 3 [{(3 a)}^{2} - {(5 b)}^{2}] = 3 (3 a + 5 b) (3 a - 5 b)$

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27 a^{2} - 75 b^{2}

27 a^{3} + \frac{1}{64 b^{3}} + \frac{27 a^{2}}{4 b} + \frac{9 a}{16 b^{2}}

a^{x^{2} - 27 a^{2}}

x = 3 a \sqrt{3}

x^{3} - 3 a x^{2} + (27 a^{2} + 9) x + 2016 = 0

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