Question

factorize 9x^2-6b^2x-(a^4-b^4)=0​

Answer 1

Correct Question :

factorize 9x²-6b²x-a⁴-b⁴ = 0.

AnsWer :

• x = b² - a² /3
• x = b² + a² /3.

SolutioN :

factorize the middle term.

→ 9x²-6b²x-a⁴-b⁴ = 0.

→ 9x² - 6b²x - a⁴ - b⁴ = 0.

→ ( 3x )² - 2( 3x )( b² ) - a⁴ + ( b² )² = 0.

→ ( 3x - b² )² - a⁴ = 0.

→ ( 3x - b² )² - ( a² )² = 0.

→ ( 3x - b² + a² )( 3x - b² - a² ) = 0.

★ Either,

3x - b² + a² = 0.

→ 3x = b² - a²

→ x = b² - a² /3

★ Or,

→ 3x - b² - a² = 0.

→ 3x = b² + a² .

→ x = b² + a² /3.

Some Formula :

• ( a + b )( a - b ) = a² - b².
• ( a + b )² = a² + b² + 2ab.
• ( a - b )² = a² + b² - 2ab.