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Question
If `(x^2 - 4)/(x^2 + 4) = 3/5`, the value of x is ______.
Options
4
± 4
`1/4`
`± 1/4`
MCQ
Fill in the Blanks
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Solution
If `(x^2 - 4)/(x^2 + 4) = 3/5`, the value of x is ± 4.
Explanation:
Given `(x^2 - 4)/(x^2 + 4) = 3/5`
Applying componendo and dividendo,
`(x^2 - 4 + x^2 + 4)/(x^2 - 4 - (x^2 + 4)) = (3 + 5)/(3 - 5)`
`\implies (2x^2)/(x^2 - 4 - x^2 - 4) = 8/(-2)`
`\implies (2x^2)/-8 = -4`
`\implies 2x^2 = 32`
`\implies x^2 = 16`
`\implies x = ±sqrt(16)`
`\implies x = ± 4`
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