Question

find the positive value of x which satisfies the equation. x+5/2-x=-3/2​

Answer 1

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Answer 2

QUESTION :

$find \: the \: positive \: value \: of \: x \: which \: satisfies \: the \: equation - - > \frac{ {x}^{2 } + 5}{2 - {x}^{2} } = - \times \frac{3}{2}$

SOLUTION :

$= > put {x}^{2} = y \: in \: the \: given \: equation. \: then \: it \: becomes \\ \\ \\ \\ \\ \\ \\ \\ \frac{y + 5}{2 - y} = - \times \frac{3}{2}$

$by \: cross \: multiplication \: we \: get$

$= > 2(y + 5) = - 3(2 - y)$

$= > 2y + 10 = - 6 + 3y$

$= > 2y - 3y = - 6 - 10$

$or$

$= > - y = - 16$

$= > y = 16$

$= > y = {x}^{2}$

$= > {x}^{2} = 16 = {4}^{2}$

$= > x = 4$

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VERIFICATION: FOR X = 4

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$l.h.s. \frac{ {x}^{2 } + 5 }{2 - {x}^{2} } = \frac{ {4}^{2} + 5}{2 - {4}^{2} } = \frac{16 + 5}{2 - 16} = \frac{21}{ - 14} = - \times \frac{3}{2} = r.h.s.$

HENCE, X = 4

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