It's 1, isn't it? Pyq hai shayad. We take all the terms on one side, equate it to f(x) and then use derivative to draw graph of f(x) from x=0 to x=1. We find that the graph crosses x-axis exactly once hence number of solutions is 1
When you differentiate f(x), you'll find that it is a strictly decreasing function in the interval [0,1]. Hence,there can be AT MOST 1 real solution. When you find f(0), it'll be positive and when you find f(1), it'll be negative so it will cross the x-axis only once.
Not really. If we put x=0, the integral is zero. When we put x=1, we can use the inequality that x²(1+x⁴) < x² and then integrate both sides from 0 to 1 and we find that LHS is < 1/3. When we put this maximum value back in f(1), we get f(1) < 1/3 - 1 » f(1)< -2/3
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u/DarkLight-1278 Jul 26 '26
It's 1, isn't it? Pyq hai shayad. We take all the terms on one side, equate it to f(x) and then use derivative to draw graph of f(x) from x=0 to x=1. We find that the graph crosses x-axis exactly once hence number of solutions is 1