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प्रश्न
Solve the following quadratic equation by completing the square method.
x2 + 2x – 5 = 0
बेरीज
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उत्तर
x2 + 2x – 5 = 0
Comparing x2 + 2x with x2 + 2xy,
2xy = 2x
∴ y = 1
∴ y2 = 1
∴ x2 + 2x + 1 is a perfect square trinomial.
x2 + 2x – 5 = 0
∴ x2 + 2x + 1 − 1 − 5 = 0
∴ (x + 1)2 − 6 = 0
∴ `(x + 1)^2 - (sqrt 6)^2` = 0
∴ `(x + 1 + sqrt 6) (x + 1 - sqrt 6)` = 0
∴ `x + 1 + sqrt 6` = 0 or `x + 1 - sqrt 6` = 0
∴ x = `-1 - sqrt 6` or x = `-1 + sqrt 6`
`-1 - sqrt 6, -1 + sqrt 6` are the roots of the given quadratic equation.
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