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प्रश्न
Solve using the quadratic formula x² – 4x + 1 = 0
उत्तर
x2 - 4x + 1 = 0
a = 1, b = -4, c = 1
x = `(-b ± sqrt(b^2 - 4ac))/(2a)`
= `(-(-4) ± sqrt((-4)^2 -4 xx 1 xx 1))/(2xx 1) `
= `(4 ± sqrt(16 - 4))/(2)`
= `(4 + sqrt(12))/(2)`
Taking (+)
= `(4 + 2sqrt(3))/(2)`
= 2 + `sqrt(3)`
∴ x = 2 + 1·732
= 3·732
Taking (-)
or x = `(4 - sqrt(12))/(2)`
= `(4 - 2sqrt(3))/(2)`
= 2 - `sqrt(3)`
∴ x = 2 - 1·732
= 0·268
Hence, x = 2 + `sqrt(3) and 2 - sqrt3)`
or 3·732 and 0·268
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