Can You Solve This System of Exponential Radical Equations? скачать в хорошем качестве

Can You Solve This System of Exponential Radical Equations?

Can you find a and b from these exponential equations? Given: 5^√(a-b) = √125 and 5^√(a+b) = √125, Find a and b This problem features two exponential equations with square roots in the exponents! There's a brilliant approach using base simplification. The key is recognizing √125 = 5^(3/2), so both equations become 5^√(a-b) = 5^(3/2) and 5^√(a+b) = 5^(3/2). This gives √(a-b) = 3/2 and √(a+b) = 3/2, meaning a-b = 9/4 and a+b = 9/4, creating a simple system to solve. 💡 Pause and try solving it before watching! This problem teaches you: ✓ Exponential equation solving ✓ Base matching techniques ✓ System with nested radicals ✓ Adding and subtracting equations ✓ Strategic simplification methods Perfect for students preparing for: • Math Olympiads (IMO, AMC, AIME) • Competition mathematics • Algebra II and Pre-Calculus courses • Anyone who loves exponential systems! The solution uses elegant base matching to simplify everything! 👍 Like if you solved it! 💬 Share your approach in the comments 🔔 Subscribe for more Olympiad problems #matholympiad #mathematics #algebra #exponentialequations #systemofequations #radicals #basematching #problemsolving #mathchallenge #competitionmath #mathpuzzle #stem #precalculus