Can You Solve This Easy Algebra Math Problem?

Algebra Math Problem: The sum of two variables and the sum of the square of three variables are given. Then find the sum of the fourth power

Solve the following algebra math problem

a+b=1

a^2+b^2=9

a^4+b^4=?

Solution: we can solve this algebra math problem in two different ways

Method 1: Using the expansion of (a + b)^2

We know, a + b = 1

So, 

(a + b)² = 1 = a² + 2ab + b² 

ie, 

1 = 9 + 2ab

So 

ab = –4

Then we get 

(a² + b²)² = a⁴ + 2a²b² + b⁴

81 = a⁴ + b⁴ + 2(ab)² = a⁴ + b⁴ + 2 × 16

So

a⁴ + b⁴ = 49

Method 2: Using the expansion of (a + b)^4

We know 

(a + b)⁴ = a⁴ + 4a³b + 6a²b² + 4ab³ + b⁴ = a⁴ + b⁴ + 4ab(a² + b²) + 6a²b²

1⁴ = a⁴ + b⁴ + 4(–4) × 9 + 6( –4)²

So

a⁴ + b⁴ = 49