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Question
Solve the following equation by factorization:
`2sqrt(5)x^2 - 3x - sqrt(5) = 0`
Sum
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Solution
Given,
⇒ `2sqrt(5)x^2 - 3x - sqrt(5) = 0`
⇒ `2sqrt(5)x^2 - 5x + 2x - sqrt(5) = 0`
⇒ `sqrt(5)x(2x - sqrt(5)) + 1(2x - sqrt(5)) = 0`
⇒ `(sqrt(5)x + 1)(2x - sqrt(5)) = 0`
⇒ `(sqrt(5)x + 1) = 0` or `(2x - sqrt(5)) = 0` ...[Using zero-product rule]
⇒ `(sqrt(5)x + 1) = 0` or `(2x - sqrt(5)) = 0`
⇒ `sqrt(5)x = -1` or `2x = sqrt(5)`
⇒ `x = (-1)/sqrt(5)` or `x = sqrt(5)/2`
Hence, `x = {sqrt(5)/2, (-1)/sqrt(5)}`.
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