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Question
Solve the following quadratic equation:
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
Sum
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Solution
Given:
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
⇒ `x^2 - x - sqrt(2)x + sqrt(2) = 0`
⇒ `x(x - 1) - sqrt(2)(x - 1) = 0`
⇒ `(x - sqrt(2))(x - 1) = 0`
⇒ `x - sqrt(2) = 0` or `x - 1 = 0`
⇒ `x = sqrt(2)` or `x = 1`
Hence, the roots of the equation are `sqrt(2)` and 1.
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