Algebraic Identities

Concept: This problem can be solved in two ways: by finding the value of first, or by using an algebraic identity.

Method 1: Finding the value of Given: Multiply the entire equation by (assuming ): Rearrange into a quadratic equation: This is a perfect square trinomial: . Taking the square root of both sides: Now that we have , we can find the value of : Method 2: Using the algebraic identity for We know the identity: . Let and . Then . And . Also, . Substitute these into the identity: We are given . Substitute this value: Now, solve for : Both methods yield the same result.