This 80th Power Algebra Problem Breaks the Moment You Stop Expanding
TUTOR H.K DASS
502 views
In this video, we solve a tricky algebra problem: given x² + y² + xy = 0, find the value of [(x − y)/√(3x)]⁸⁰ + [(x − y)/√(3y)]⁸⁰. This question looks intimidating at first glance because of the high exponent (power 80) and the nested radicals, but it becomes surprisingly manageable once you set k = x/y and rewrite the entire equation in terms of that single variable. We break the problem down step by step, showing you exactly how to turn the given condition into a simple equation in k, simplify the radical expressions using that substitution, and carry the exponent rules through cleanly to reach the final answer without getting lost in messy algebra.
This kind of problem shows up often in competitive exams, Olympiad-style question papers, and advanced algebra courses, so if you're preparing for exams or just enjoy a good algebraic challenge, this walkthrough will sharpen your skills with substitution techniques, exponent rules, and identity manipulation. Make sure to watch until the end so you don't miss the key substitution trick that makes this whole problem click. If you found this helpful, like the video, subscribe to Tutor H.K Dass for more algebra and advanced math tutorials, and drop a comment if you'd like more problems like this one.
#Algebra #MathTutorial #AlgebraTricks #Mathematics #ExamPrep
2 Comments
k⁴⁰ = k^(13·3+1) = k^(13·3) · k
But (k³)^(13+1) = (k³)^14 = k⁴²
You got that wrong at 11:45, as an exponent is evaluated as if it had brackets around it.
Better make k⁴⁰ = k³⁹ · k first, before using 39 = 13 · 3.
This 80th Power Algebra Problem Breaks the Moment You Stop Expanding
TUTOR H.K DASS
502 views
In this video, we solve a tricky algebra problem: given x² + y² + xy = 0, find the value of [(x − y)/√(3x)]⁸⁰ + [(x − y)/√(3y)]⁸⁰. This question looks intimidating at first glance because of the high exponent (power 80) and the nested radicals, but it becomes surprisingly manageable once you set k = x/y and rewrite the entire equation in terms of that single variable. We break the problem down step by step, showing you exactly how to turn the given condition into a simple equation in k, simplify the radical expressions using that substitution, and carry the exponent rules through cleanly to reach the final answer without getting lost in messy algebra.
This kind of problem shows up often in competitive exams, Olympiad-style question papers, and advanced algebra courses, so if you're preparing for exams or just enjoy a good algebraic challenge, this walkthrough will sharpen your skills with substitution techniques, exponent rules, and identity manipulation. Make sure to watch until the end so you don't miss the key substitution trick that makes this whole problem click. If you found this helpful, like the video, subscribe to Tutor H.K Dass for more algebra and advanced math tutorials, and drop a comment if you'd like more problems like this one.
#Algebra #MathTutorial #AlgebraTricks #Mathematics #ExamPrep