asnwer=2x

The long way to solve this is to expand the left hand side (LHS) using the binomial expansion of (x+y)⁴ that has coefficients of 1:4:6:4:1. The x⁴ term will appear on both sides and cancel out to leave a cubic equation with lots of powers of 4, which are factored out. In the original form, it's easy to see that 2 is a solution, so (x-2) can be factored out from the cubic equation, leaving a quadratic equation, which can be solved by the quadratic formula. Instead of all that work, or factoring the difference of squares, I came up with a shortcut. Since both sides are raised to the 4th power, I took the 4th root, and made sure to put in the 4 roots of 1: (x-4)⁴ = x⁴ = 1⁴ * x⁴ x-4 = ±x, ±i*x x±x = 4; x*(1±i) = 4 2*x = 4; 0 = 4; x = 4/(1±i) x = 2; ∅; x = 2*(1±i) x = 2, 2±2*i

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2

Решается в уме

X=2

Should it not be 4 roots in this equation?

一看就知道有2