Question

Find the roots of the equation (x² + 3x)² – (x² + 3x) –6 = 0.

please solve with explaination​

Answer 1

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Answer 2

Given equation is (x2 + 3x)2 – (x2 + 3x) – 6 = 0

Putting x2 + 3x = y , the given equation becomes

y2 – y – 6 = 0

⇒ y2 – 3y + 2y – 6 = 0

⇒ y(y – 3) + 2(y – 3) = 0

⇒ (y – 3)(y + 2) = 0

⇒ y – 3 = 0 or y + 2 = 0

⇒ y = 3 or y = - 2

But x2 + 3x = y