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Question
Solve the following equation by factorisation :
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
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Solution
`sqrt(3)x^2 + 10x + 7sqrt(3)` = 0
⇒ `sqrt(3)x^2 + 3x + 7x + 7sqrt(3)` = 0
⇒ `sqrt(3)x(x + sqrt(3)) + 7(x + sqrt(3))` = 0
⇒ `(x + sqrt(3))(sqrt(3) + 7)` = 0
Either `x + sqrt(3)` = 0,
then x = `-sqrt(3)`
or
`sqrt(3) x + 7` = 0,
then `sqrt(3)x` = –7
⇒ x = `(-7)/sqrt(3)`
x = `(-7 xx sqrt(3))/(sqrt(3) xx sqrt(3)`
= `(-7sqrt(3))/(3)`
Hence x = `-sqrt(3), (-7sqrt(3))/(3)`.
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