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Question
Solve the following equation by using formula :
`2x^2 + sqrt(5) - 5` = 0
Solution
`2x^2 + sqrt(5) - 5` = 0
Here a = 2, b = `sqrt(5)`, c = -5
D = b2 - 4ac
= `(sqrt(5))^2 - 4 xx 2 xx (-5)`
= 5 + 40
= 45
∵ x = `(-b ± sqrt("D"))/(2a)`
= `(-sqrt(5) ± sqrt(45))/(2 xx 2)`
= `(-sqrt(5) ± sqrt(9 xx 5))/(4)`
= `(-sqrt(5) ± 3sqrt(5))/(4)`
∴ x1 = `(-sqrt(5) + 3sqrt(5))/(4)`
= `(2sqrt(5))/(4)`
= `sqrt(5)/(2)`
x2 = `(-sqrt(5) - 3sqrt(5))/(4)`
= `(-4sqrt(5))/(4)`
= `-sqrt(5)`
Hence x = `sqrt(5)/(2), -sqrt(5)`.
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