Question

A challenge For all Aryabhatta's and Moderators .

Ans - 7 , -17/2 .

Don't Spam . Did it on your own intelligence​

Answer 1

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$\huge {AηsωeR}$

$\bf \: \frac{2}{2a + 1} \int_0^1x^adx = \frac{1}{60}$

$\bf \: \frac{2}{2a + 1} [ \frac{ {x}^{a + 1} }{a + 1} ]_ {0}^{1} = \frac{1}{60}$

$\bf \: \frac{2}{2a + 1} \times \frac{1}{a + 1} = \frac{1}{60}$

$\bf\implies \:(2a + 1)(a + 1) = 120$

$\bf \:2 {a}^{2} + 3a + 1 = 120$

$\bf \:  ⟼ 2 {a}^{2} + 3a - 119 = 0$

$\bf \:a = \dfrac{ - 3 \: ± \: \sqrt{9 + 952} }{4}$

$\bf \:a = \dfrac{ - 3 \: ± \: 31}{4}$

$\bf \:a = \dfrac{ - 3 + 31}{4} \: and \: \dfrac{ - 3 - 31}{4}$

$\bf\implies \:a = 7 \: and \: - \dfrac{17}{2}$

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