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Question
Solve the following equation by factorization:
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
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Solution 1
`x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
⇒ `x^2 - x - sqrt(2)x + sqrt(2) = 0`
⇒ `(x - 1) - sqrt(2) (x - 1)= 0`
⇒ `(x - 1) (x - sqrt(2)) = 0`
Either x – 1 = 0,
Then x = 1
or
`x - sqrt(2) = 0`,
Then x = `sqrt(2)`
Hence x = 1, `sqrt(2)`.
Solution 2
Given,
⇒ `x^2 - (1 + sqrt(2))x + sqrt(2) = 0`
⇒ `x^2 - 1x - 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 ...[Using zero-product rule]
⇒ `x = sqrt(2)` or x = 1
Hence, `x = {1, sqrt(2)}`.
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