If the set of all a in R, for which the equat | vedclass

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Question

$(a-5)^2-8(15-3 a)<0$
$a^2+14 a+25-120<0$
$a^2+14 a-95<0$
$(a+19)(a-5)<0$
$a \in(-19,5)$
$	herefore-19$
$	herefore \sum_{x \in X }

Vedclass · Accepted Answer

$2139$

Vedclass · Answer

$(a-5)^2-8(15-3 a)<0$
$a^2+14 a+25-120<0$
$a^2+14 a-95<0$
$(a+19)(a-5)<0$
$a \in(-19,5)$
$	herefore-19$
$	herefore \sum_{x \in X } x^2=\left(1^2+2^2+\ldots .+4^2ight)+\left(1^2+2^2+\ldots+18^2ight)$
$=\frac{4 	imes 5 	imes 9}{6}+\frac{18 	imes 19 	imes 37}{6}$
$=30+2109$
$=2139$

If the set of all $a \in R$, for which the equation $2 x^2+$ $(a-5) x+15=3 a$ has no real root, is the interval $(\alpha, \beta)$, and $X=\{x \in Z: \alpha < x < \beta\}$, then $\sum_{x \in X} x^2$ is equal to

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