Question

can someone help me with conjugates in algebra

Answer 1

In algebra, a conjugate is a binomial formed by negating the second term of a binomial. The conjugate of x + y is x − y, where x and y are real numbers. If y is imaginary, the process is termed complex conjugation: the complex conjugate of a + bi is a − bi, where a and b are real.

Answer 2

Try\[\frac{6}{\sqrt{2}-\sqrt{3}} \times \frac{\sqrt{2}+\sqrt{3}}{\sqrt{2}+\sqrt{3}}\]

Answer 3

Let's do it this way,
\[\frac{6}{\sqrt{2}-\sqrt{3}} \]
Multiply both numerator and denominator by -1 first
\[\frac{-6}{\sqrt{3}-\sqrt{2}}\]
Then
\[\frac{-6}{\sqrt{3}-\sqrt{2}} \times \frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}+\sqrt{2}}\]

Answer 4

\[\frac{-6(\sqrt{3}+\sqrt{2})}{(\sqrt{3}-\sqrt{2})(\sqrt{3}+\sqrt{2})}\]

Answer 5

\[=\frac{-6(\sqrt{3}+\sqrt{2})}{3+\sqrt{6}-\sqrt{6}-2} \]
Hence,
\[=\frac{-6(\sqrt{3}+\sqrt{2})}{1}\]
\[=-6(\sqrt{3}+\sqrt{2})\]

Answer 6

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Answer 7

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Answer 8

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Answer 9

Thanks :)

Answer 10

welcome