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प्रश्न
Solve the following quadratic equation:
`sqrt(7)x^2 - 6x - 13sqrt(7) = 0`
योग
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उत्तर
We write, –6x = 7x – 13x as `sqrt(7)x^2 xx (-13sqrt(7)) = 91x^2 = 7x xx (-13x)`
∴ `sqrt(7)x^2 - 6x - 13sqrt(7) = 0`
⇒ `sqrt(7)x^2 + 7x - 13x - 13sqrt(7) = 0`
⇒ `sqrt(7)x(x + sqrt(7)) - 13(x + sqrt(7)) = 0`
⇒ `(x + sqrt(7))(sqrt(7)x - 13) = 0`
⇒ `x + sqrt(7) = 0` or `sqrt(7)x - 13 = 0`
⇒ `x = -sqrt(7)` or `x = 13/sqrt(7) = (13sqrt(7))/7`
Hence, the roots of the given equation are `-sqrt(7)` and `(13sqrt(7))/7`.
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