Understanding Two Substitutions Convert A Fraction Into Quadratic Math Olympiad
Let's dive into the details surrounding Two Substitutions Convert A Fraction Into Quadratic Math Olympiad. (3x²-3x+18)/10=√(x³+8) → Find all real x Factor x³+8 first. x³+8=(x+
Key Takeaways about Two Substitutions Convert A Fraction Into Quadratic Math Olympiad
- Math Olympiad
- (x-1)+√(x+3)+
- Radical
- Smart observation, nested radicals,
- (x-
Detailed Analysis of Two Substitutions Convert A Fraction Into Quadratic Math Olympiad
(x²+54x+9)/(x+3)=14√x → Find all values of x Let t=√x so x=t². Cross multiplication, quartic factoring, x^(2x)+x^x=756 → Find x Notice x^(2x)=(x^x)². Let a=x^x. Equation: a²+a-756=0. Factor: (a+28)(a-27)=0. a=27 or a=-28. So a=-28 ...
[x/(x-1)]²+[x/(x+1)]²=10/9 → Find all values of x Let a=x/(x-1) and b=x/(x+1). Then a²+b²=10/9. Compute a+b and ab: a+b=2x²/(x²-1).
That wraps up our extensive overview of Two Substitutions Convert A Fraction Into Quadratic Math Olympiad.