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प्रश्न
Solve the quadratic equation: `x^2 + 2sqrt(2)x - 6` = 0 for x.
उत्तर
We have, `x^2 + 2sqrt(2)x - 6` = 0
Now, by using the formula x = `(-b +- sqrt(b^2 - 4ac))/(2a)`, we get
x = `(-2sqrt(2) +- sqrt((2sqrt(2))^2 - 4 xx 1 xx (-6)))/(2 xx 1)`
⇒ x = `(-2sqrt(2) +- sqrt(8 + 24))/2`
⇒ x = `(-2sqrt(2) +- 4sqrt(2))/2`
= `- sqrt(2) +- 2sqrt(2)`
⇒ x = `-sqrt(2) + 2sqrt(2)`, x = `-sqrt(2) - 2sqrt(2)`
⇒ x = `sqrt(2)`, x = `-3sqrt(2)`
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