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प्रश्न
Solve:
(x2 – x)2 + 5(x2 – x) + 4 = 0
उत्तर
(x2 – x)2 + 5(x2 – x) + 4 = 0
Let x2 – x = y
Then y2 + 5y + 4 = 0
`=>` y2 + 4y + y + 4 = 0
`=>` y(y + 4) + 1(y + 4) = 0
`=>` (y + 4)(y + 1) = 0
If y + 4 = 0 or y + 1 = 0
`=>` x2 – x + 4 = 0 or x2 – x + 1 = 0
`=> x = (-(-1)+-sqrt((-1)^2 - 4(1)(4)))/(2(1))` or `(-(-1) +- sqrt((-1)^2 - 4(1)(1)))/(2(1))`
`=> x = (1 +- sqrt(-15))/2 ("reject")` or `x = (1 +- sqrt(-3))/2 ("reject")`
∴ Given equation has no real solution
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