What would be the value of x to make 37.68 × 37.68 + 37.68 × x × x + 0.32 × 0.32 to be a perfect square?
0.8
The correct answer is 0.8.
Square of a Sum: $(a+b)^2 = a^2 + 2ab + b^2$ Square of a Difference: $(a-b)^2 = a^2 - 2ab + b^2$ Difference of Squares: $a^2 - b^2 = (a-b)(a+b)$ Cube of a Sum: $(a+b)^3 = a^3 + 3a^2b + 3ab^2 + b^3$ Cube of a Difference: $(a-b)^3 = a^3 - 3a^2b + 3ab^2 - b^3$ Recognizing these identities can simplify complex algebraic expressions and equations, making problems like finding the value of $x$ for a perfect square much easier to solve.
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