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प्रश्न
Solve:
(x2 – 3x)2 – 16(x2 – 3x) – 36 = 0
उत्तर
(x2 – 3x)2 – 16(x2 – 3x) – 36 = 0
Let x2 – 3x = y
Then y2 – 16y – 36 = 0
`=>` y2 – 18y + 2y – 36 = 0
`=>` y(y – 18) + 2(y – 18) = 0
`=>` (y – 18)(y + 2) = 0
If y – 18 = 0 or y + 2= 0
`=>` x2 – 3x – 18 = 0 or x2 – 3x + 2 = 0
`=>` x2 – 6x + 3x – 18 = 0 or x2 – 2x – x + 2 = 0
`=>` x(x – 6) + 3(x – 6) = 0 or x(x – 2) – 1(x – 2) = 0
`=>` (x – 6)(x + 3) = 0 or (x – 2)(x – 1) = 0
If x – 6 = 0 or x + 3 = 0 or x – 2 = 0 or x – 1 = 0
Then x = 6 or x = – 3 or x = 2 or x = 1
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