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Question
Which constant must be added and subtracted to solve the quadratic equation `9x^2 + 3/4x - sqrt(2) = 0` by the method of completing the square?
Options
`1/8`
`1/64`
`1/4`
`9/64`
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Solution
`bb(1/64)`
Explanation:
Given equation is `9x^2 + 3/4x - sqrt(2)` = 0
`(3x)^2 + 1/4 (3x) - sqrt(2)` = 0
On putting 3x = y,
We have `y^2 + 1/4y - sqrt(2)` = 0
`y^2 + 1/4y + (1/8)^2 - (1/8)^2 - sqrt(2)` = 0
`(y + 1/8)^2 = 1/64 + sqrt(2)`
`(y + 1/8)^2 = (1 + 64 sqrt(2))/64`
Thus, `1/64` must be added and subtracted to solve the given equation.
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