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Solve the following quadratic equations by factorization:\(a(x^{2}+1)-x(a^2+1)=0\)

Answer»

In factorization, we write the middle term of the quadratic equation either as a sum of two numbers or difference of two numbers such that the equation can be factorized.

\(a(x^{2}+1)-x(a^2+1)=0\)

⇒ ax2 + a – a2x – x = 0 

⇒ ax2 – x(a2 + 1) + a = 0 

⇒ ax(x – a) – 1(x – a) = 0 

⇒ (ax – 1)(x – a) = 0 

⇒ x = 1/a, a



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