Question

The product of $\sqrt{x}+2\sqrt{y}$ with its conjugate is?

• A. $x+4y$
• B. $x-4y$
• C. $x+2y$
• D. $x-2y$

Answer 1

Answer: (B)

$x-4y$

The sum and difference of two simple quadratic surds are said to be conjugate of each other.

The conjuate of $\sqrt{x}+2\sqrt{y}$ is $\sqrt{x}-2\sqrt{y}$

Use the algebric properties, $(a-b)(a+b)=a^2-b^2$

Product of $\sqrt{x}+2\sqrt{y}$ with $\sqrt{x}-2\sqrt{y}$ is equal to $(\sqrt{x}{)}^2-(\sqrt{2y}{)}^2=x-4y$