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Question
In each of the following, determine whether the given numbers are solutions of the given equation or not: `x^2 - sqrt(2)x - 4 = 0, x = -sqrt(2),2sqrt(2)`
Solution
`x^2 - sqrt(2)x - 4 = 0, x = -sqrt(2),2sqrt(2)`
(a) x = `-sqrt(2)`
Substituting x = `-sqrt(2)`
L.H.S. = `x^2 - sqrt(2)x - 4`
= `(-sqrt(2))^2 - sqrt(2) (-sqrt(2)) -4`
= 2 + 2 - 4
= 0
= R.H.S.
∴ x = `-sqrt(2)` is its solution.
(b) x = `-2sqrt(2)`
Substituting x = `-2sqrt(2)`
L.H.S. = `x^2 - sqrt(2)x - 4`
= `(-2sqrt(2))^2 - sqrt(2) (-2sqrt(2)) - 4`
= 8 - 4 - 4
= 8 - 8
= 0
= R.H.S.
∴ x = `-2sqrt(2)` is its solution.
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