Question: If xy = 1, what is the value of \(\frac{2^{(x + y)^2}}{2^{(x-y)^2}}\)?
Correct Answer: D
Approach Solution (1):
\(\frac{2^{(x + y)^2}}{2^{(x-y)^2}}=2^{(x + y)^2-(x-y)^2}=2^{(x+y+x+y)(x+y-x+y)}=2^{(2x)(2y)}=2^{4xy}=2^4=16\)
Approach Solution (2):
\(\frac{2^{(x + y)^2}}{2^{(x-y)^2}}\)
\(=\frac{2^{x^2+y^2+2xy}}{2^{x^2+y^2-2xy}}\)
\(=2^{(x^2+y^2+2xy)-(x^2+y^2-2xy)}\)
\(=2^{x^2+y^2+2xy-x^2-y^2+2xy}\)
\(=2^{4xy}=2^4=16\)
“If xy = 1, what is the value of \(\frac{2^{(x + y)^2}}{2^{(x-y)^2}}\)?”- is a topic of the GMAT Quantitative reasoning section of GMAT. This question has been taken from the book “GMAT Official Guide Quantitative Review”. To solve GMAT Problem Solving questions a student must have knowledge about a good amount of qualitative skills. The GMAT Quant topic in the problem-solving part requires calculative mathematical problems that should be solved with proper mathematical knowledge.
Suggested GMAT Problem Solving Samples
*The article might have information for the previous academic years, please refer the official website of the exam.