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kicyunya [14]
3 years ago
11

Find the product of the 3+ V11 and its conjugate.

Mathematics
1 answer:
erik [133]3 years ago
6 0

Answer:

It would be -2.

Step-by-step explanation:

<u>Key skills: Conjugate, Distribution Property, and Addition/Subtraction </u>

3 + \sqrt{11\\} is your expression. The conjugate is an important concept you need to know to solve this.

Given the expression: a + \sqrt{b\\}

It's conjugate would be: a - \sqrt{b}

(Basically if there is an addition sign between the 2 terms, it would become a subtractions symbol and if there is a subtraction symbol it would become an addition symbol)

1) So the conjugate of  3+ \sqrt{11} would be 3 - \sqrt{11}

2) Now we would have to multiply them

  • (3 + \sqrt{11})(3- \sqrt{11}) is your expression.
  • If you use distribution property, you will get to: 3^{2} + 3\sqrt{11} - 3\sqrt{11} + \sqrt{11}^{2}
  • The two middle terms would cancel out (they both add up to 0), so then we have 3^{2} - \sqrt{11}^2
  • This would simplify into 9-11, which is then <u><em>-2</em></u>

Hope you understood, and have a nice day!! :)

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