Question

X-b/a-b=x²/a²
btw answers are: a; ab/a-b.
can someone explain
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Answer 1

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Answer:

x = {a, ab/(a-b)}

Explanation:

Cross-multiply, then solve the quadratic using the quadratic formula.

`(x-b)/(a-b)=(x^2)/(a^2)\\\\a^2(x-b)=x^2(a-b)\\\\(a-b)x^2-a^2x+a^2b=0\\\\x=(a^2\pm√(a^4-4(a-b)a^2b))/(2(a-b))=(a^2\pm√(a^2(a^2-4ab+4b^2)))/(2(a-b))\\\\=(a(a\pm (a-2b))/(2(a-b))=\left\{(a\cdot 2(a-b))/(2(a-b)),\ (a(2b))/(2(a-b))\right\}\\\\ \boxed{x=\left\{a,\ (ab)/(a-b)\right\}}`