Question

Positive value of the variable for which the given is satisfied $\sf{\dfrac{3-x^2}{8+x^2}=\dfrac{-3}{4}.}$​

Answer 1

$\;\;\underline{\textbf{\textsf{ Given:-}}}$

•$\sf{\dfrac{3-x^2}{8+x^2}=\dfrac{-3}{4}}$

$\;\;\underline{\textbf{\textsf{ To Find :-}}}$

• What's the positive value of the variable?

$\;\;\underline{\textbf{\textsf{ Solution :-}}}$

Given that,

$:\implies{\sf{\dfrac{3-x^2}{8+x^2}=\dfrac{-3}{4}}} \\ \\ : \implies{\sf{ 4(3-x^2) = - 3(8+x^2)}} \\ \\: \implies{\sf{ 12-4x^2 = - 24 - 3x^2}} \\ \\: \implies{\sf{ 12 + 24= - 3x^2+ 4x^2 }} \\ \\: \implies{\sf{36 = x ^2 }} \\ \\ : \implies{\sf{ \sqrt{36} = x }} \\ \\ : \implies{\sf{6 = x }} \\ \\ \\ \tt{ \green{ :\implies X = 6}}$

$\:\:\:\:\dag\bf{\underline{\underline \green{therefore :-}}}$

Positive value of the variable = 6

____________________________________________

$\;\;\underline{\textbf{\textsf{ Verification :-}}}$

We have ,

• Positive value of the variable = 6

$\:\:\:\:\dag\bf{\underline \green{Putting\:the\:value:-}}$

$: \implies{\sf{\dfrac{3-6^2}{8+6^2}=\dfrac{-3}{4}}} \\ \\ : \implies{\sf{ \dfrac{3-36}{8+36}=\dfrac{-3}{4}}} \\ \\ :\implies{\sf{ \dfrac{-33}{44}=\dfrac{-3}{4}}} \\ \\ : \implies{\sf{ \dfrac{-3}{4}=\dfrac{-3}{4}}}\\ \\: \implies{\boxed{\tt{LHS = RHS}}}$

$\:\:\:\:\dag\bf{\underline{\underline \green{Hence:-}}}$

(Verified)