To find the value of a^2 + b^2, we need to square the given equations:
a^2 + 2ab + b^2 = 49a^2 + b^2 = 49 - 2aba^2 + b^2 = 49 - 2(2)a^2 + b^2 = 45
Next, to find the value of a^3 + b^3, we need to cube the given equations:
a^3 + 3a^2b + 3ab^2 + b^3 = 343a^3 + b^3 = 343 - 3a^2b - 3ab^2a^3 + b^3 = 343 - 3(2) - 3(2)a^3 + b^3 = 343 - 6 - 6a^3 + b^3 = 331
Therefore, a^2 + b^2 = 45 and a^3 + b^3 = 331.
To find the value of a^2 + b^2, we need to square the given equations:
a^2 + 2ab + b^2 = 49
a^2 + b^2 = 49 - 2ab
a^2 + b^2 = 49 - 2(2)
a^2 + b^2 = 45
Next, to find the value of a^3 + b^3, we need to cube the given equations:
a^3 + 3a^2b + 3ab^2 + b^3 = 343
a^3 + b^3 = 343 - 3a^2b - 3ab^2
a^3 + b^3 = 343 - 3(2) - 3(2)
a^3 + b^3 = 343 - 6 - 6
a^3 + b^3 = 331
Therefore, a^2 + b^2 = 45 and a^3 + b^3 = 331.