-step explanation:Here a + 1/a = 5 is GIVEN,Here a + 1/a = 5 is given,LET we do square on both sidesHere a + 1/a = 5 is given,Let we do square on both sides(a + 1/a)² = 5²Here a + 1/a = 5 is given,Let we do square on both sides(a + 1/a)² = 5²a² + 1/a² + 2(a²)(1/a²) = 25a² + 1/a² = 25 - 2a² + 1/a² = 25 - 2a² + 1/a² = 23a² + 1/a² = 25 - 2a² + 1/a² = 23Again, doing square on both sidesa² + 1/a² = 25 - 2a² + 1/a² = 23Again, doing square on both sides(a² + 1/a²)² = 23²a² + 1/a² = 25 - 2a² + 1/a² = 23Again, doing square on both sides(a² + 1/a²)² = 23²a⁴ + 1/a⁴ + 2(a⁴)(1/a⁴) = 529a² + 1/a² = 25 - 2a² + 1/a² = 23Again, doing square on both sides(a² + 1/a²)² = 23²a⁴ + 1/a⁴ + 2(a⁴)(1/a⁴) = 529a⁴ + 1/a⁴ = 529 - 2a² + 1/a² = 25 - 2a² + 1/a² = 23Again, doing square on both sides(a² + 1/a²)² = 23²a⁴ + 1/a⁴ + 2(a⁴)(1/a⁴) = 529a⁴ + 1/a⁴ = 529 - 2Hence,a² + 1/a² = 25 - 2a² + 1/a² = 23Again, doing square on both sides(a² + 1/a²)² = 23²a⁴ + 1/a⁴ + 2(a⁴)(1/a⁴) = 529a⁴ + 1/a⁴ = 529 - 2Hence,a⁴ + 1/a⁴ = 527 HOPE YOU ARE SATISFIED BY THIS SOLUTION. THANK YOU HAVE A GREAT WEEKEND.