Solve the following quadratic equation for x:\( x^{2}-4 a x-b^{2}+4 a^

1.	Solve the following quadratic equation for x:\( x^{2}-4 a x-b^{2}+4 a^{2}=0 \)
Answer» x² - 4ax - b² + 4a² = 0 ⇒ x² - 4ax + 4a² - b² = 0 ⇒ (x - 2a)² - b² = 0 (\(\because\) a² - 2ab + b² = (a - b)²) ⇒ (x - 2a - b) (x - 2a + b) = 0 (\(\because\) a² - b² = (a - b) (a + b)) ⇒ (x - 2a - b) or x - 2a + b = 0 ⇒ x = 2a + b or x = 2a - b Hence, solution of given quadratic equation are x = 2a + b and x = 2a - b.

Solve the following quadratic equation for x:\( x^{2}-4 a x-b^{2}+4 a^{2}=0 \)

Answer»

x² - 4ax - b² + 4a² = 0

⇒ x² - 4ax + 4a² - b² = 0

⇒ (x - 2a)² - b² = 0 (\(\because\) a² - 2ab + b² = (a - b)²)

⇒ (x - 2a - b) (x - 2a + b) = 0 (\(\because\) a² - b² = (a - b) (a + b))

⇒ (x - 2a - b) or x - 2a + b = 0

⇒ x = 2a + b or x = 2a - b

Hence, solution of given quadratic equation are x = 2a + b and x = 2a - b.

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Solve the following quadratic equation for x:\( x^{2}-4 a x-b^{2}+4 a^{2}=0 \)

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