To solve this problem, we can use the formula for the square of a binomial, which is (a + b)^2 = a^2 + 2ab + b^2.

Given that (f + g)^2 = 54, we can expand this to f^2 + 2fg + g^2 = 54.

We are also given that 2fg = 24.

Substituting 2fg = 24 into the expanded binomial gives us f^2 + 24 + g^2 = 54.

Solving for f^2 + g^2, we subtract 24 from both sides to get f^2 + g^2 = 54 - 24 = 30.

So, f^2 + g^2 = 30, which corresponds to answer choice (D) 30.

Question

To solve this problem, we can use the formula for the square of a binomial, which is (a + b)^2 = a^2 + 2ab + b^2.

Given that (f + g)^2 = 54, we can expand this to f^2 + 2fg + g^2 = 54.

We are also given that 2fg = 24.

Substituting 2fg = 24 into the expanded binomial gives us f^2 + 24 + g^2 = 54.

Solving for f^2 + g^2, we subtract 24 from both sides to get f^2 + g^2 = 54 - 24 = 30.

So, f^2 + g^2 = 30, which corresponds to answer choice (D) 30.

Knowee AI · Accepted Answer

To solve this problem, we can use the formula for the square of a binomial, which is (a + b)^2 = a^2 + 2ab + b^2.

Given that (f + g)^2 = 54, we can expand this to f^2 + 2fg + g^2 = 54.

We are also given that 2fg = 24.

Substituting 2fg = 24 into the expanded binomial gives us f^2 + 24 + g^2 = 54.

Solving for f^2 + g^2, we subtract 24 from both sides to get f^2 + g^2 = 54 - 24 = 30.

So, f^2 + g^2 = 30, which corresponds to answer choice (D) 30.

If f and g are positive, (f + g)2 = 54 and 2fg = 24, what is f2 + g2?(A) 6(B) 12(C) 15(D) 30(E) 78