Question

Solve this equation:a²(x-b)/a-b-x²=b²(a-x)/b-a ​

Answer 1

Answer:

a²/x-b + b²/x-a =a+b

Let’s x<>a and x<>b

a²(x-a) + b²(x-b) =(a+b)(x-a)(x-b)

a²x-a^3+ b²x-b^3 =ax^2 - a^2x-abx +a^2*b+bx^2 -abx - b^2x +a*b^2

(a+b)x^2 - 2(a^2+ab+b^2)x+(a^3+a^2*b+a*b^2+b^3)=0

Let’s a+b<>0

x1,2={2(a^2+ab+b^2)+-sqrt[4(a^2+ab+b^2)^2–4(a+b)(a^3+a^2*b+a*b^2+b^3)]}/[2(a+b)]=

={2(a^2+ab+b^2)+-sqrt[4(a^2*b^2)]}/[2(a+b)] =

=(a^2+ab+b^2)+-sqrt(a^2*b^2)/(a+b)=

=(a^2+ab+b^2+-ab)/(a+b)

x1=a+b

x2=(a^2+b^2)/(a+b)

If a+b=0 i.e. b=-a then

a²/x+a + a²/x-a =0

x+a+x-a=2x=0

x=0

So

If a+b=0 then x=0

else

x1=a+b

x2=(a^2+b^2)/(a+b)

Step-by-step explanation:

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Answer 2

Answer:

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