9514 1404 393
Answer:
x = {a, ab/(a-b)}
Step-by-step explanation:
Cross-multiply, then solve the quadratic using the quadratic formula.
[tex]\dfrac{x-b}{a-b}=\dfrac{x^2}{a^2}\\\\a^2(x-b)=x^2(a-b)\\\\(a-b)x^2-a^2x+a^2b=0\\\\x=\dfrac{a^2\pm\sqrt{a^4-4(a-b)a^2b}}{2(a-b)}=\dfrac{a^2\pm\sqrt{a^2(a^2-4ab+4b^2)}}{2(a-b)}\\\\=\dfrac{a(a\pm (a-2b)}{2(a-b)}=\left\{\dfrac{a\cdot 2(a-b)}{2(a-b)},\ \dfrac{a(2b)}{2(a-b)}\right\}\\\\ \boxed{x=\left\{a,\ \dfrac{ab}{a-b}\right\}}[/tex]
