The value of ^2 20^ + ^4 20^ ^4 20^ + ^2 20^ is

Step-by-step solution

Let = 20^ . The expression is E = ² + ⁴ ⁴ + ² . Using the identity ² = 1 - ² , we substitute into the numerator: Numerator = (1 - ² ) + ⁴ = 1 - ² + ⁴ . Using the identity ² = 1 - ² , we substitute into the denominator: Denominator = ⁴ + (1 - ² ) = 1 - ² + ⁴ . Since ² = 1 - ² , the numerator becomes 1 - (1 - ² ) + (1 - ² )² = 1 - 1 + ² + 1 - 2 ² + ⁴ = 1 - ² + ⁴ . Thus, the numerator is equal to the denominator, so E = 1 . Answer: 1