Solve the quadratic equations by formula 1 `a(x^2+1) = (a^2+1)x` , a is not 0 2 `4x^2 - 4ax+(a^2-b^2)=0`

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embizze | High School Teacher | (Level 2) Educator Emeritus

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(1) `a(x^2+1)=(a^2+1)x`


`ax^2-(a^2+1)x+a=0`  Use the quadratic formula:

If `ax^2+bx+c=0` then `x=(-b+-sqrt(b^2-4ac))/(2a)`

Here `a=a,b=-(a^2+1),c=a` so






so `x=(a^2+1+a^2-1)/(2a)=(2a^2)/(2a)=a`



(2) `4x^2-4ax+(a^2-b^2)=0`

Here a=4,b=-4a and `c=a^2+b^2`





so `x=1/2(a+b)` or `1/2(a-b)`

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