Solve for x: 4x2 + 20ax + 25a2 - 36b2 = 0.

1.	Solve for x: 4x2 + 20ax + 25a2 - 36b2 = 0.
Answer» 4x² + 20 ax + 25a²- 36b² = 0 ⇒ (2x)² + 2 \(\times\) 2x \(\times\) 5a + (5a)² = 36b² ⇒ (2x + 5a)² = (6b)² (\(\because\) a² + 2ab + b² = (a + b)²) ⇒ 2x + 5a = 6b or 2x + 5a = -6b ⇒ 2x = 6b - 5a or 2x = -6b - 5a ⇒ x = \(\frac{6b-5a}2\) or x = \(\frac{-6b-5a}2=\frac{-1}2\)(6b + 5a) Hence, root of the given equation are \(\frac{6b-5a}2\) or \(\frac{-1}2\) (6b + 5a)

Answer»

4x² + 20 ax + 25a²- 36b² = 0

⇒ (2x)² + 2 \(\times\) 2x \(\times\) 5a + (5a)² = 36b²

⇒ (2x + 5a)² = (6b)² (\(\because\) a² + 2ab + b² = (a + b)²)

⇒ 2x + 5a = 6b or 2x + 5a = -6b

⇒ 2x = 6b - 5a or 2x = -6b - 5a

⇒ x = \(\frac{6b-5a}2\) or x = \(\frac{-6b-5a}2=\frac{-1}2\)(6b + 5a)

Hence, root of the given equation are

\(\frac{6b-5a}2\) or \(\frac{-1}2\) (6b + 5a)

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Solve for x: 4x2 + 20ax + 25a2 - 36b2 = 0.

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