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प्रश्न
Solve the following quadratic equation.
`1/(4 - "p") - 1/(2 + "p") = 1/4`
उत्तर
`1/(4 - "p") - 1/(2 + "p") = 1/4`
∴ `(2 + "p" - (4 - "p"))/((4 - "p")(2 + "p")) = 1/4`
∴ `(2 + "p" - 4 + "p")/(8 + 4"p" - 2"p" - "p"^2) = 1/4`
∴ `(2"p" - 2)/(8 + 2"p" - "p"^2) = 1/4`
∴ 4(2p – 2) = 8 + 2p – p2
∴ 8p – 8 = 8 + 2p – p2
∴ p2 – 2p + 8p – 8 – 8 = 0
∴ p2 + 6p – 16 = 0
| -16 |
| 8 -2 |
| 8 × (-2) = -16 |
| 8 - 2 = 6 |
∴ p2 + 8p – 2p – 16 = 0
∴ p(p + 8) – 2(p + 8) = 0
∴ (p + 8)(p – 2) = 0
By using the property, if the product of two numbers is zero, then at least one of them is zero, we get
p + 8 = 0 or p – 2 = 0
∴ p = – 8 or p = 2
∴ The roots of the given equation are – 8 and 2.
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