# Find a Positive Value of X for Which the Given Equation is Satisfied: X 2 − 9 5 + X 2 = − 5 9 - Mathematics

Sum

Find a positive value of x for which the given equation is satisfied:

$\frac{x^2 - 9}{5 + x^2} = - \frac{5}{9}$

#### Solution

$\frac{x^2 - 9}{5 + x^2} = \frac{- 5}{9}$
$\text{ or }9 x^2 - 81 = - 25 - 5 x^2 [\text{ After cross multiplication }]$
$\text{ or }9 x^2 + 5 x^2 = - 25 + 81$
$\text{ or }14 x^2 = 56$
$\text{ or }x^2 = \frac{56}{14}$
$\text{ or }x^2 = 4 = 2^2$
$\text{ or }x = 2$
$\text{ Thus, }x = 2\text{ is the solution of the given equation . }$
$\text{ Check: }$
$\text{ Substituting }x = 2\text{ in the given equation, we get: }$
$\text{ L . H . S . }= \frac{2^2 - 9}{5 + 2^2} = \frac{4 - 9}{5 + 4} = \frac{- 5}{9}$
$\text{ R . H . S . }= \frac{- 5}{9}$
$\therefore\text{ L . H . S . = R . H . S . for }x = 2 .$

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#### APPEARS IN

RD Sharma Class 8 Maths
Chapter 9 Linear Equation in One Variable
Exercise 9.3 | Q 24.1 | Page 17